diff --git a/cggmp21/src/key_refresh.rs b/cggmp21/src/key_refresh.rs
index d025554..586cea1 100644
--- a/cggmp21/src/key_refresh.rs
+++ b/cggmp21/src/key_refresh.rs
@@ -1,106 +1,24 @@
+mod aux_only;
+mod non_threshold;
+
 use digest::Digest;
-use futures::SinkExt;
-use generic_ec::{
-    hash_to_curve::{self, FromHash},
-    Curve, Point, Scalar, SecretScalar,
-};
-use generic_ec_zkp::{hash_commitment::HashCommit, schnorr_pok};
-use paillier_zk::{
-    libpaillier, no_small_factor::non_interactive as π_fac, paillier_blum_modulus as π_mod,
-    unknown_order::BigNumber, BigNumberExt, SafePaillierDecryptionExt, SafePaillierEncryptionExt,
-};
+use generic_ec::{hash_to_curve::FromHash, Curve, Scalar};
+use paillier_zk::unknown_order::BigNumber;
 use rand_core::{CryptoRng, RngCore};
-use round_based::{
-    rounds_router::{simple_store::RoundInput, RoundsRouter},
-    Delivery, Mpc, MpcParty, Outgoing,
-};
+use round_based::Mpc;
 use thiserror::Error;
 
 use crate::{
     errors::IoError,
-    execution_id::ProtocolChoice,
-    key_share::{AnyKeyShare, DirtyIncompleteKeyShare, DirtyKeyShare, KeyShare, PartyAux},
+    key_share::{AnyKeyShare, AuxInfo, DirtyIncompleteKeyShare, KeyShare},
     progress::Tracer,
     security_level::SecurityLevel,
-    utils,
-    utils::{
-        but_nth, collect_blame, collect_simple_blame, iter_peers, scalar_to_bignumber, xor_array,
-        AbortBlame,
-    },
-    zk::ring_pedersen_parameters as π_prm,
+    utils::AbortBlame,
     ExecutionId,
 };
 
-use self::msg::*;
-
-#[doc = include_str!("../docs/mpc_message.md")]
-pub mod msg {
-    use digest::Digest;
-    use generic_ec::{Curve, Point};
-    use generic_ec_zkp::{
-        hash_commitment::{self, HashCommit},
-        schnorr_pok,
-    };
-    use paillier_zk::{
-        no_small_factor::non_interactive as π_fac, paillier_blum_modulus as π_mod,
-        unknown_order::BigNumber,
-    };
-    use round_based::ProtocolMessage;
-
-    use crate::{security_level::SecurityLevel, zk::ring_pedersen_parameters as π_prm};
-
-    /// Message of key refresh protocol
-    #[derive(ProtocolMessage, Clone)]
-    // 3 kilobytes for the largest option, and 2.5 kilobytes for second largest
-    #[allow(clippy::large_enum_variant)]
-    pub enum Msg<E: Curve, D: Digest, L: SecurityLevel> {
-        Round1(MsgRound1<D>),
-        Round2(MsgRound2<E, D, L>),
-        Round3(MsgRound3<E>),
-    }
-
-    /// Message from round 1
-    #[derive(Clone)]
-    pub struct MsgRound1<D: Digest> {
-        pub commitment: HashCommit<D>,
-    }
-    /// Message from round 2
-    #[derive(Clone)]
-    pub struct MsgRound2<E: Curve, D: Digest, L: SecurityLevel> {
-        /// **X_i** in paper
-        pub Xs: Vec<Point<E>>,
-        /// **A_i** in paper
-        pub sch_commits_a: Vec<schnorr_pok::Commit<E>>,
-        pub N: BigNumber,
-        pub s: BigNumber,
-        pub t: BigNumber,
-        /// psi_circonflexe_i in paper
-        // this should be L::M instead, but no rustc support yet
-        pub params_proof: π_prm::Proof<{ π_prm::SECURITY }>,
-        /// rho_i in paper
-        // ideally it would be [u8; L::SECURITY_BYTES], but no rustc support yet
-        pub rho_bytes: L::Rid,
-        /// u_i in paper
-        pub decommit: hash_commitment::DecommitNonce<D>,
-    }
-    /// Unicast message of round 3, sent to each participant
-    #[derive(Clone)]
-    pub struct MsgRound3<E: Curve> {
-        /// psi_i in paper
-        // this should be L::M instead, but no rustc support yet
-        pub mod_proof: (π_mod::Commitment, π_mod::Proof<{ π_prm::SECURITY }>),
-        /// phi_i^j in paper
-        pub fac_proof: π_fac::Proof,
-        /// C_i^j in paper
-        pub C: BigNumber,
-        /// psi_i_j in paper
-        ///
-        /// Here in the paper you only send one proof, but later they require you to
-        /// verify by all the other proofs, that are never sent. We fix this here
-        /// and require each party to send every proof to everyone
-        pub sch_proofs_x: Vec<schnorr_pok::Proof<E>>,
-    }
-}
+pub type AuxOnlyMsg<D> = aux_only::Msg<D>;
+pub type NonThresholdMsg<E, L, D> = non_threshold::Msg<E, L, D>;
 
 /// To speed up computations, it's possible to supply data to the algorithm
 /// generated ahead of time
@@ -134,18 +52,35 @@ impl<L: SecurityLevel> PregeneratedPrimes<L> {
     }
 }
 
-pub struct KeyRefreshBuilder<'a, E, L, D>
+/// A variant of [`GenericKeyRefreshBuilder`] that performs key refresh
+pub type KeyRefreshBuilder<'a, E, L, D> =
+    GenericKeyRefreshBuilder<'a, E, L, D, RefreshShare<'a, E, L>>;
+
+/// A variant of [`GenericKeyRefreshBuilder`] that only generates auxiliary info
+/// and doesn't require key shares
+pub type AuxInfoGenerationBuilder<'a, E, L, D> = GenericKeyRefreshBuilder<'a, E, L, D, AuxOnly>;
+
+/// Entry point for key refresh and auxiliary info generation.
+pub struct GenericKeyRefreshBuilder<'a, E, L, D, M>
 where
     E: Curve,
     L: SecurityLevel,
     D: Digest,
 {
-    core_share: &'a DirtyIncompleteKeyShare<E, L>,
+    target: M,
     execution_id: ExecutionId<E, L, D>,
     pregenerated: PregeneratedPrimes<L>,
     tracer: Option<&'a mut dyn Tracer>,
 }
 
+/// A marker for [`KeyRefreshBuilder`]
+pub struct RefreshShare<'a, E: Curve, L: SecurityLevel>(&'a DirtyIncompleteKeyShare<E, L>);
+/// A marker for [`AuxInfoGenerationBuilder`]
+pub struct AuxOnly {
+    i: u16,
+    n: u16,
+}
+
 impl<'a, E, L, D> KeyRefreshBuilder<'a, E, L, D>
 where
     E: Curve,
@@ -157,534 +92,106 @@ where
     /// PregeneratedPrimes can be obtained with [`PregeneratedPrimes::generate`]
     pub fn new(key_share: &'a impl AnyKeyShare<E, L>, pregenerated: PregeneratedPrimes<L>) -> Self {
         Self {
-            core_share: key_share.core(),
+            target: RefreshShare(key_share.core()),
             execution_id: Default::default(),
             pregenerated,
             tracer: None,
         }
     }
 
-    /// Specifies another hash function to use
-    ///
-    /// _Caution_: this function overwrites [execution ID](Self::set_execution_id). Make sure
-    /// you specify execution ID **after** calling this function.
-    pub fn set_digest<D2: Digest>(self) -> KeyRefreshBuilder<'a, E, L, D2> {
-        KeyRefreshBuilder {
-            core_share: self.core_share,
-            execution_id: Default::default(),
-            pregenerated: self.pregenerated,
-            tracer: None,
-        }
-    }
-
-    pub fn set_execution_id(self, execution_id: ExecutionId<E, L, D>) -> Self {
-        Self {
-            execution_id,
-            ..self
-        }
-    }
-
-    pub fn set_progress_tracer(mut self, tracer: &'a mut dyn Tracer) -> Self {
-        self.tracer = Some(tracer);
-        self
-    }
-
     /// Carry out the refresh procedure. Takes a lot of time
     pub async fn start<R, M>(self, rng: &mut R, party: M) -> Result<KeyShare<E, L>, KeyRefreshError>
     where
         R: RngCore + CryptoRng,
-        M: Mpc<ProtocolMessage = Msg<E, D, L>>,
+        M: Mpc<ProtocolMessage = NonThresholdMsg<E, D, L>>,
         E: Curve,
         Scalar<E>: FromHash,
         L: SecurityLevel,
         D: Digest<OutputSize = digest::typenum::U32> + Clone + 'static,
     {
-        run_refresh(
+        non_threshold::run_refresh(
             rng,
             party,
             self.execution_id,
             self.pregenerated,
             self.tracer,
-            self.core_share,
+            self.target.0,
         )
         .await
     }
 }
 
-async fn run_refresh<R, M, E, L, D>(
-    mut rng: &mut R,
-    party: M,
-    execution_id: ExecutionId<E, L, D>,
-    pregenerated: PregeneratedPrimes<L>,
-    mut tracer: Option<&mut dyn Tracer>,
-    core_share: &DirtyIncompleteKeyShare<E, L>,
-) -> Result<KeyShare<E, L>, KeyRefreshError>
+impl<'a, E, L, D> GenericKeyRefreshBuilder<'a, E, L, D, AuxOnly>
 where
-    R: RngCore + CryptoRng,
-    M: Mpc<ProtocolMessage = Msg<E, D, L>>,
     E: Curve,
-    Scalar<E>: FromHash,
     L: SecurityLevel,
-    D: Digest<OutputSize = digest::typenum::U32> + Clone + 'static,
+    D: Digest,
 {
-    tracer.protocol_begins();
-
-    tracer.stage("Retrieve auxiliary data");
-    let i = core_share.i;
-    let n = u16::try_from(core_share.public_shares.len()).map_err(|_| Bug::TooManyParties)?;
-
-    tracer.stage("Setup networking");
-    let MpcParty { delivery, .. } = party.into_party();
-    let (incomings, mut outgoings) = delivery.split();
-
-    let mut rounds = RoundsRouter::<Msg<E, D, L>>::builder();
-    let round1 = rounds.add_round(RoundInput::<MsgRound1<D>>::broadcast(i, n));
-    let round2 = rounds.add_round(RoundInput::<MsgRound2<E, D, L>>::broadcast(i, n));
-    let round3 = rounds.add_round(RoundInput::<MsgRound3<E>>::p2p(i, n));
-    let mut rounds = rounds.listen(incomings);
-
-    tracer.stage("Precompute execution id and shared state");
-    let execution_id = execution_id.evaluate(ProtocolChoice::Keygen);
-    let sid = execution_id.as_slice();
-    let tag_htc = hash_to_curve::Tag::new(&execution_id).ok_or(Bug::InvalidHashToCurveTag)?;
-    let parties_shared_state = D::new_with_prefix(execution_id);
-
-    // Round 1
-    tracer.round_begins();
-
-    tracer.stage("Retrieve primes (p and q)");
-    let PregeneratedPrimes { p, q, .. } = pregenerated;
-    tracer.stage("Compute paillier decryption key (N)");
-    let N = &p * &q;
-    let phi_N = (&p - 1) * (&q - 1);
-    let dec =
-        libpaillier::DecryptionKey::with_primes_unchecked(&p, &q).ok_or(Bug::PaillierKeyError)?;
-
-    // *x_i* in paper
-    tracer.stage("Generate secret x_i and public X_i");
-    // generate n-1 values first..
-    let mut xs = (0..n - 1)
-        .map(|_| SecretScalar::<E>::random(rng))
-        .collect::<Vec<_>>();
-    // then create a last element such that the sum is zero
-    let mut x_last = -xs.iter().sum::<Scalar<E>>();
-    xs.push(SecretScalar::new(&mut x_last));
-    debug_assert_eq!(xs.iter().sum::<Scalar<E>>(), Scalar::zero());
-    // *X_i* in paper
-    let Xs = xs
-        .iter()
-        .map(|x| Point::generator() * x)
-        .collect::<Vec<_>>();
-
-    tracer.stage("Generate auxiliary params r, λ, t, s");
-    let r = utils::sample_bigint_in_mult_group(rng, &N);
-    let lambda = BigNumber::from_rng(&phi_N, rng);
-    let t = r.modmul(&r, &N);
-    let s = t.powmod(&lambda, &N).map_err(|_| Bug::PowMod)?;
-
-    tracer.stage("Prove Πprm (ψˆ_i)");
-    let hat_psi = π_prm::prove(
-        parties_shared_state.clone(),
-        &mut rng,
-        π_prm::Data {
-            N: &N,
-            s: &s,
-            t: &t,
-        },
-        &phi_N,
-        &lambda,
-    )
-    .map_err(Bug::PiPrm)?;
-
-    tracer.stage("Compute schnorr commitment τ_j");
-    // tau_j and A_i^j in paper
-    let (taus, As) = (0..n)
-        .map(|_| schnorr_pok::prover_commits_ephemeral_secret::<E, _>(rng))
-        .unzip::<_, _, Vec<_>, Vec<_>>();
-
-    tracer.stage("Sample random bytes");
-    // rho_i in paper, this signer's share of bytes
-    let mut rho_bytes = L::Rid::default();
-    rng.fill_bytes(rho_bytes.as_mut());
-
-    tracer.stage("Compute hash commitment and sample decommitment");
-    // V_i and u_i in paper
-    // TODO: decommitment should be kappa bits
-    let (hash_commit, decommit) = HashCommit::<D>::builder()
-        .mix_bytes(sid)
-        .mix(n)
-        .mix(i)
-        .mix_many(&Xs)
-        .mix_many(As.iter().map(|a| a.0))
-        .mix_bytes(&N.to_bytes())
-        .mix_bytes(&s.to_bytes())
-        .mix_bytes(&t.to_bytes())
-        .mix_many_bytes(hat_psi.commitment.iter().map(|x| x.to_bytes()))
-        .mix_many_bytes(hat_psi.zs.iter().map(|x| x.to_bytes()))
-        .mix_bytes(&rho_bytes)
-        .commit(rng);
-
-    tracer.send_msg();
-    let commitment = MsgRound1 {
-        commitment: hash_commit,
-    };
-    outgoings
-        .send(Outgoing::broadcast(Msg::Round1(commitment.clone())))
-        .await
-        .map_err(IoError::send_message)?;
-    tracer.msg_sent();
-
-    // Round 2
-    tracer.round_begins();
-
-    tracer.receive_msgs();
-    let commitments = rounds
-        .complete(round1)
-        .await
-        .map_err(IoError::receive_message)?;
-    tracer.msgs_received();
-    tracer.send_msg();
-    let decommitment = MsgRound2 {
-        Xs: Xs.clone(),
-        sch_commits_a: As.clone(),
-        N: N.clone(),
-        s: s.clone(),
-        t: t.clone(),
-        params_proof: hat_psi,
-        rho_bytes: rho_bytes.clone(),
-        decommit,
-    };
-    outgoings
-        .send(Outgoing::broadcast(Msg::Round2(decommitment.clone())))
-        .await
-        .map_err(IoError::send_message)?;
-    tracer.msg_sent();
-
-    // Round 3
-    tracer.round_begins();
-
-    tracer.receive_msgs();
-    let decommitments = rounds
-        .complete(round2)
-        .await
-        .map_err(IoError::receive_message)?;
-    tracer.msgs_received();
-
-    // validate decommitments
-    tracer.stage("Validate round 1 decommitments");
-    let blame = collect_blame(&decommitments, &commitments, |j, decomm, comm| {
-        HashCommit::<D>::builder()
-            .mix_bytes(sid)
-            .mix(n)
-            .mix(j)
-            .mix_many(&decomm.Xs)
-            .mix_many(decomm.sch_commits_a.iter().map(|a| a.0))
-            .mix_bytes(decomm.N.to_bytes())
-            .mix_bytes(decomm.s.to_bytes())
-            .mix_bytes(decomm.t.to_bytes())
-            .mix_many_bytes(decomm.params_proof.commitment.iter().map(|x| x.to_bytes()))
-            .mix_many_bytes(decomm.params_proof.zs.iter().map(|x| x.to_bytes()))
-            .mix_bytes(&decomm.rho_bytes)
-            .verify(&comm.commitment, &decomm.decommit)
-            .is_err()
-    });
-    if !blame.is_empty() {
-        return Err(ProtocolAborted::invalid_decommitment(blame).into());
-    }
-    // Validate parties didn't skip any data
-    tracer.stage("Validate data sizes");
-    let blame = collect_simple_blame(&decommitments, |decommitment| {
-        let n = usize::from(n);
-        decommitment.Xs.len() != n || decommitment.sch_commits_a.len() != n
-    });
-    if !blame.is_empty() {
-        return Err(ProtocolAborted::invalid_data_size(blame).into());
-    }
-    // validate parameters and param_proofs
-    tracer.stage("Validate П_prm (ψ_i)");
-    let blame = collect_simple_blame(&decommitments, |d| {
-        if d.N.bit_length() < L::SECURITY_BYTES {
-            true
-        } else {
-            let data = π_prm::Data {
-                N: &d.N,
-                s: &d.s,
-                t: &d.t,
-            };
-            π_prm::verify(parties_shared_state.clone(), data, &d.params_proof).is_err()
+    /// Build key aux info generation operation. Start it with [`start`](Self::start).
+    ///
+    /// PregeneratedPrimes can be obtained with [`PregeneratedPrimes::generate`]
+    pub fn new_aux_gen(i: u16, n: u16, pregenerated: PregeneratedPrimes<L>) -> Self {
+        Self {
+            target: AuxOnly { i, n },
+            execution_id: Default::default(),
+            pregenerated,
+            tracer: None,
         }
-    });
-    if !blame.is_empty() {
-        return Err(ProtocolAborted::invalid_ring_pedersen_parameters(blame).into());
     }
-    // validate Xs add to zero
-    tracer.stage("Validate X_i");
-    let blame = collect_simple_blame(&decommitments, |d| {
-        d.Xs.iter().sum::<Point<E>>() != Point::zero()
-    });
-    if !blame.is_empty() {
-        return Err(ProtocolAborted::invalid_x(blame).into());
-    }
-
-    tracer.stage("Compute paillier encryption keys");
-    // encryption keys for each party
-    let encs = decommitments
-        .iter()
-        .map(|d| utils::encryption_key_from_n(&d.N))
-        .collect::<Vec<_>>();
 
-    tracer.stage("Add together shared random bytes");
-    // rho in paper, collective random bytes
-    let rho_bytes = decommitments
-        .iter()
-        .map(|d| &d.rho_bytes)
-        .fold(rho_bytes, xor_array);
-
-    // common data for messages
-    tracer.stage("Compute П_mod (ψ_i)");
-    let psi = π_mod::non_interactive::prove(
-        parties_shared_state.clone(),
-        &π_mod::Data { n: N.clone() },
-        &π_mod::PrivateData {
-            p: p.clone(),
-            q: q.clone(),
-        },
-        &mut rng,
-    )
-    .map_err(Bug::PiMod)?;
-    tracer.stage("Assemble security params for П_fac (ф_i)");
-    let π_fac_security = π_fac::SecurityParams {
-        l: L::ELL,
-        epsilon: L::EPSILON,
-        q: L::q(),
-    };
-    let n_sqrt = utils::sqrt(&N);
-    tracer.stage("Compute schnorr proof ψ_i^j");
-    let challenge = Scalar::<E>::hash_concat(tag_htc, &[&i.to_be_bytes(), rho_bytes.as_ref()])
-        .map_err(Bug::HashToScalarError)?;
-    let challenge = schnorr_pok::Challenge { nonce: challenge };
-    let psis = xs
-        .iter()
-        .zip(taus.iter())
-        .map(|(x_j, secret_j)| schnorr_pok::prove(secret_j, &challenge, x_j))
-        .collect::<Vec<_>>();
-    tracer.stage("Prepare auxiliary params and security level for proofs");
-    // message to each party
-    let iterator =
-        // use every share except ours
-        but_nth(i, xs.iter())
-        .zip(&encs)
-        .zip(decommitments.iter())
-        .zip(iter_peers(i, n));
-    for (((x, enc), d), j) in iterator {
-        tracer.stage("Paillier encryption of x_i^j");
-        let (C, _) = enc
-            .encrypt_with_random(&scalar_to_bignumber(x), &mut rng)
-            .map_err(|_| Bug::PaillierEnc)?;
-        tracer.stage("Compute П_fac (ф_i^j)");
-        let phi = π_fac::prove(
-            parties_shared_state.clone(),
-            &π_fac::Aux {
-                s: d.s.clone(),
-                t: d.t.clone(),
-                rsa_modulo: d.N.clone(),
-            },
-            π_fac::Data {
-                n: &N,
-                n_root: &n_sqrt,
-            },
-            π_fac::PrivateData { p: &p, q: &q },
-            &π_fac_security,
-            &mut rng,
+    /// Carry out the aux info generation procedure. Takes a lot of time
+    pub async fn start<R, M>(self, rng: &mut R, party: M) -> Result<AuxInfo, KeyRefreshError>
+    where
+        R: RngCore + CryptoRng,
+        M: Mpc<ProtocolMessage = aux_only::Msg<D>>,
+        E: Curve,
+        Scalar<E>: FromHash,
+        L: SecurityLevel,
+        D: Digest<OutputSize = digest::typenum::U32> + Clone + 'static,
+    {
+        aux_only::run_aux_gen(
+            self.target.i,
+            self.target.n,
+            rng,
+            party,
+            self.execution_id,
+            self.pregenerated,
+            self.tracer,
         )
-        .map_err(Bug::PiFac)?;
-
-        tracer.send_msg();
-        let msg = MsgRound3 {
-            mod_proof: psi.clone(),
-            fac_proof: phi.clone(),
-            sch_proofs_x: psis.clone(),
-            C,
-        };
-        outgoings
-            .send(Outgoing::p2p(j, Msg::Round3(msg)))
-            .await
-            .map_err(IoError::send_message)?;
-        tracer.msg_sent();
-    }
-
-    // Output
-    tracer.round_begins();
-
-    tracer.receive_msgs();
-    let shares_msg_b = rounds
-        .complete(round3)
         .await
-        .map_err(IoError::receive_message)?;
-    tracer.msgs_received();
-
-    tracer.stage("Paillier decrypt x_j^i from C_j^i");
-    // x_j^i in paper. x_i^i is a share from self to self, so it was never sent,
-    // so it's handled separately
-    let my_share = &xs[usize::from(i)];
-    // If the share couldn't be decrypted, abort with a faulty party
-    let (shares, blame) =
-        utils::partition_results(shares_msg_b.iter_indexed().map(|(j, mid, m)| {
-            let bigint = dec
-                .decrypt_to_bigint(&m.C)
-                .map_err(|_| AbortBlame::new(j, mid, mid))?;
-            Ok::<_, AbortBlame>(bigint.to_scalar())
-        }));
-    if !blame.is_empty() {
-        return Err(ProtocolAborted::paillier_dec(blame).into());
-    }
-    debug_assert_eq!(shares.len(), usize::from(n) - 1);
-
-    tracer.stage("Validate shares");
-    // verify shares are well-formed
-    let blame = shares
-        .iter()
-        .zip(decommitments.iter_indexed())
-        .filter_map(|(share, (j, msg_id, decommitment))| {
-            let i = usize::from(i);
-            let X = Point::generator() * share;
-            if X != decommitment.Xs[i] {
-                Some(AbortBlame::new(j, msg_id, msg_id))
-            } else {
-                None
-            }
-        })
-        .collect::<Vec<_>>();
-    if !blame.is_empty() {
-        return Err(ProtocolAborted::invalid_x_share(blame).into());
     }
-    // It is possible at this point to report a bad party to others, but we
-    // don't implement it now
-
-    tracer.stage("Validate schnorr proofs п_j and ψ_j^k");
-    // verify sch proofs for x
-    let blame = utils::try_collect_blame(
-        &decommitments,
-        &shares_msg_b,
-        |j, decommitment, proof_msg| {
-            let challenge =
-                Scalar::<E>::hash_concat(tag_htc, &[&j.to_be_bytes(), rho_bytes.as_ref()])
-                    .map_err(Bug::HashToScalarError)?;
-            let challenge = schnorr_pok::Challenge { nonce: challenge };
+}
 
-            // x length is verified above
-            if proof_msg.sch_proofs_x.len() != decommitment.Xs.len() {
-                return Ok(true);
-            }
-            // proof for x, i.e. psi_j^k for every k
-            let iterator = proof_msg
-                .sch_proofs_x
-                .iter()
-                .zip(&decommitment.Xs)
-                .zip(&decommitment.sch_commits_a);
-            for ((sch_proof, x), commit) in iterator {
-                if sch_proof.verify(commit, &challenge, x).is_err() {
-                    return Ok(true);
-                }
-            }
-            // explicit type ascription because it can't get inferred
-            Ok::<_, Bug>(false)
-        },
-    )?;
-    if !blame.is_empty() {
-        return Err(ProtocolAborted::invalid_schnorr_proof(blame).into());
+impl<'a, E, L, D, T> GenericKeyRefreshBuilder<'a, E, L, D, T>
+where
+    E: Curve,
+    L: SecurityLevel,
+    D: Digest,
+{
+    /// Specifies another hash function to use
+    ///
+    /// _Caution_: this function overwrites [execution ID](Self::set_execution_id). Make sure
+    /// you specify execution ID **after** calling this function.
+    pub fn set_digest<D2: Digest>(self) -> GenericKeyRefreshBuilder<'a, E, L, D2, T> {
+        GenericKeyRefreshBuilder {
+            target: self.target,
+            execution_id: Default::default(),
+            pregenerated: self.pregenerated,
+            tracer: None,
+        }
     }
 
-    tracer.stage("Validate ψ_j (П_mod)");
-    // verify mod proofs
-    let blame = collect_blame(
-        &decommitments,
-        &shares_msg_b,
-        |_, decommitment, proof_msg| {
-            let data = π_mod::Data {
-                n: decommitment.N.clone(),
-            };
-            let (comm, proof) = &proof_msg.mod_proof;
-            π_mod::non_interactive::verify(parties_shared_state.clone(), &data, comm, proof)
-                .is_err()
-        },
-    );
-    if !blame.is_empty() {
-        return Err(ProtocolAborted::invalid_mod_proof(blame).into());
+    pub fn set_execution_id(self, execution_id: ExecutionId<E, L, D>) -> Self {
+        Self {
+            execution_id,
+            ..self
+        }
     }
 
-    tracer.stage("Validate ф_j (П_fac)");
-    // verify fac proofs
-    let blame = collect_blame(
-        &decommitments,
-        &shares_msg_b,
-        |_, decommitment, proof_msg| {
-            π_fac::verify(
-                parties_shared_state.clone(),
-                &π_fac::Aux {
-                    s: s.clone(),
-                    t: t.clone(),
-                    rsa_modulo: N.clone(),
-                },
-                π_fac::Data {
-                    n: &decommitment.N,
-                    n_root: &utils::sqrt(&decommitment.N),
-                },
-                &π_fac_security,
-                &proof_msg.fac_proof,
-            )
-            .is_err()
-        },
-    );
-    if !blame.is_empty() {
-        return Err(ProtocolAborted::invalid_fac_proof(blame).into());
+    pub fn set_progress_tracer(mut self, tracer: &'a mut dyn Tracer) -> Self {
+        self.tracer = Some(tracer);
+        self
     }
-
-    // verifications passed, compute final key shares
-
-    let old_core_share = core_share.clone();
-    tracer.stage("Calculate new x_i");
-    let x_sum = shares.iter().sum::<Scalar<E>>() + my_share;
-    let mut x_star = old_core_share.x + x_sum;
-    tracer.stage("Calculate new X_i");
-    let X_sums = (0..n).map(|k| {
-        let k = usize::from(k);
-        decommitments
-            .iter_including_me(&decommitment)
-            .map(|d| d.Xs[k])
-            .sum::<Point<E>>()
-    });
-    let X_stars = old_core_share
-        .public_shares
-        .into_iter()
-        .zip(X_sums)
-        .map(|(x, p)| x + p)
-        .collect();
-
-    tracer.stage("Assemble new core share");
-    let new_core_share = DirtyIncompleteKeyShare {
-        public_shares: X_stars,
-        x: SecretScalar::new(&mut x_star),
-        ..old_core_share
-    };
-    tracer.stage("Assemble auxiliary info");
-    let party_auxes = decommitments
-        .iter_including_me(&decommitment)
-        .map(|d| PartyAux {
-            N: d.N.clone(),
-            s: d.s.clone(),
-            t: d.t.clone(),
-        })
-        .collect();
-    let key_share = DirtyKeyShare {
-        core: new_core_share,
-        p,
-        q,
-        parties: party_auxes,
-    };
-
-    tracer.protocol_ends();
-    Ok(key_share.try_into().map_err(Bug::InvalidShareGenerated)?)
 }
 
 #[derive(Debug, Error)]
diff --git a/cggmp21/src/key_refresh/aux_only.rs b/cggmp21/src/key_refresh/aux_only.rs
new file mode 100644
index 0000000..f382e50
--- /dev/null
+++ b/cggmp21/src/key_refresh/aux_only.rs
@@ -0,0 +1,351 @@
+use digest::Digest;
+use futures::SinkExt;
+use generic_ec::Curve;
+use generic_ec_zkp::hash_commitment::{self, HashCommit};
+use paillier_zk::{
+    no_small_factor::non_interactive as π_fac, paillier_blum_modulus as π_mod,
+    unknown_order::BigNumber, BigNumberExt,
+};
+use rand_core::{CryptoRng, RngCore};
+use round_based::{
+    rounds_router::{simple_store::RoundInput, RoundsRouter},
+    Delivery, Mpc, MpcParty, Outgoing, ProtocolMessage,
+};
+
+use crate::{
+    errors::IoError,
+    execution_id::ProtocolChoice,
+    key_share::{AuxInfo, DirtyAuxInfo, PartyAux},
+    progress::Tracer,
+    security_level::SecurityLevel,
+    utils,
+    utils::{collect_blame, collect_simple_blame},
+    zk::ring_pedersen_parameters as π_prm,
+    ExecutionId,
+};
+
+use super::{Bug, KeyRefreshError, PregeneratedPrimes, ProtocolAborted};
+
+/// Message of key refresh protocol
+#[derive(ProtocolMessage, Clone)]
+// 3 kilobytes for the largest option, and 2.5 kilobytes for second largest
+#[allow(clippy::large_enum_variant)]
+pub enum Msg<D: Digest> {
+    Round1(MsgRound1<D>),
+    Round2(MsgRound2<D>),
+    Round3(MsgRound3),
+}
+
+/// Message from round 1
+#[derive(Clone)]
+pub struct MsgRound1<D: Digest> {
+    commitment: HashCommit<D>,
+}
+/// Message from round 2
+#[derive(Clone)]
+pub struct MsgRound2<D: Digest> {
+    N: BigNumber,
+    s: BigNumber,
+    t: BigNumber,
+    /// psi_circonflexe_i in paper
+    // this should be L::M instead, but no rustc support yet
+    params_proof: π_prm::Proof<{ π_prm::SECURITY }>,
+    /// u_i in paper
+    decommit: hash_commitment::DecommitNonce<D>,
+}
+/// Unicast message of round 3, sent to each participant
+#[derive(Clone)]
+pub struct MsgRound3 {
+    /// psi_i in paper
+    // this should be L::M instead, but no rustc support yet
+    mod_proof: (π_mod::Commitment, π_mod::Proof<{ π_prm::SECURITY }>),
+    /// phi_i^j in paper
+    fac_proof: π_fac::Proof,
+}
+
+pub async fn run_aux_gen<R, M, E, L, D>(
+    i: u16,
+    n: u16,
+    mut rng: &mut R,
+    party: M,
+    execution_id: ExecutionId<E, L, D>,
+    pregenerated: PregeneratedPrimes<L>,
+    mut tracer: Option<&mut dyn Tracer>,
+) -> Result<AuxInfo, KeyRefreshError>
+where
+    R: RngCore + CryptoRng,
+    M: Mpc<ProtocolMessage = Msg<D>>,
+    E: Curve,
+    L: SecurityLevel,
+    D: Digest<OutputSize = digest::typenum::U32> + Clone + 'static,
+{
+    tracer.protocol_begins();
+
+    tracer.stage("Retrieve auxiliary data");
+
+    tracer.stage("Setup networking");
+    let MpcParty { delivery, .. } = party.into_party();
+    let (incomings, mut outgoings) = delivery.split();
+
+    let mut rounds = RoundsRouter::<Msg<D>>::builder();
+    let round1 = rounds.add_round(RoundInput::<MsgRound1<D>>::broadcast(i, n));
+    let round2 = rounds.add_round(RoundInput::<MsgRound2<D>>::broadcast(i, n));
+    let round3 = rounds.add_round(RoundInput::<MsgRound3>::p2p(i, n));
+    let mut rounds = rounds.listen(incomings);
+
+    tracer.stage("Precompute execution id and shared state");
+    let execution_id = execution_id.evaluate(ProtocolChoice::Keygen);
+    let sid = execution_id.as_slice();
+    let parties_shared_state = D::new_with_prefix(execution_id);
+
+    // Round 1
+    tracer.round_begins();
+
+    tracer.stage("Retrieve primes (p and q)");
+    let PregeneratedPrimes { p, q, .. } = pregenerated;
+    tracer.stage("Compute paillier decryption key (N)");
+    let N = &p * &q;
+    let phi_N = (&p - 1) * (&q - 1);
+
+    tracer.stage("Generate auxiliary params r, λ, t, s");
+    let r = utils::sample_bigint_in_mult_group(rng, &N);
+    let lambda = BigNumber::from_rng(&phi_N, rng);
+    let t = r.modmul(&r, &N);
+    let s = t.powmod(&lambda, &N).map_err(|_| Bug::PowMod)?;
+
+    tracer.stage("Prove Πprm (ψˆ_i)");
+    let hat_psi = π_prm::prove(
+        parties_shared_state.clone(),
+        &mut rng,
+        π_prm::Data {
+            N: &N,
+            s: &s,
+            t: &t,
+        },
+        &phi_N,
+        &lambda,
+    )
+    .map_err(Bug::PiPrm)?;
+
+    tracer.stage("Compute hash commitment and sample decommitment");
+    // V_i and u_i in paper
+    // TODO: decommitment should be kappa bits
+    let (hash_commit, decommit) = HashCommit::<D>::builder()
+        .mix_bytes(sid)
+        .mix(n)
+        .mix(i)
+        .mix_bytes(&N.to_bytes())
+        .mix_bytes(&s.to_bytes())
+        .mix_bytes(&t.to_bytes())
+        .mix_many_bytes(hat_psi.commitment.iter().map(|x| x.to_bytes()))
+        .mix_many_bytes(hat_psi.zs.iter().map(|x| x.to_bytes()))
+        .commit(rng);
+
+    tracer.send_msg();
+    let commitment = MsgRound1 {
+        commitment: hash_commit,
+    };
+    outgoings
+        .send(Outgoing::broadcast(Msg::Round1(commitment.clone())))
+        .await
+        .map_err(IoError::send_message)?;
+    tracer.msg_sent();
+
+    // Round 2
+    tracer.round_begins();
+
+    tracer.receive_msgs();
+    let commitments = rounds
+        .complete(round1)
+        .await
+        .map_err(IoError::receive_message)?;
+    tracer.msgs_received();
+    tracer.send_msg();
+    let decommitment = MsgRound2 {
+        N: N.clone(),
+        s: s.clone(),
+        t: t.clone(),
+        params_proof: hat_psi,
+        decommit,
+    };
+    outgoings
+        .send(Outgoing::broadcast(Msg::Round2(decommitment.clone())))
+        .await
+        .map_err(IoError::send_message)?;
+    tracer.msg_sent();
+
+    // Round 3
+    tracer.round_begins();
+
+    tracer.receive_msgs();
+    let decommitments = rounds
+        .complete(round2)
+        .await
+        .map_err(IoError::receive_message)?;
+    tracer.msgs_received();
+
+    // validate decommitments
+    tracer.stage("Validate round 1 decommitments");
+    let blame = collect_blame(&decommitments, &commitments, |j, decomm, comm| {
+        HashCommit::<D>::builder()
+            .mix_bytes(sid)
+            .mix(n)
+            .mix(j)
+            .mix_bytes(decomm.N.to_bytes())
+            .mix_bytes(decomm.s.to_bytes())
+            .mix_bytes(decomm.t.to_bytes())
+            .mix_many_bytes(decomm.params_proof.commitment.iter().map(|x| x.to_bytes()))
+            .mix_many_bytes(decomm.params_proof.zs.iter().map(|x| x.to_bytes()))
+            .verify(&comm.commitment, &decomm.decommit)
+            .is_err()
+    });
+    if !blame.is_empty() {
+        return Err(ProtocolAborted::invalid_decommitment(blame).into());
+    }
+    // validate parameters and param_proofs
+    tracer.stage("Validate П_prm (ψ_i)");
+    let blame = collect_simple_blame(&decommitments, |d| {
+        if d.N.bit_length() < L::SECURITY_BYTES {
+            true
+        } else {
+            let data = π_prm::Data {
+                N: &d.N,
+                s: &d.s,
+                t: &d.t,
+            };
+            π_prm::verify(parties_shared_state.clone(), data, &d.params_proof).is_err()
+        }
+    });
+    if !blame.is_empty() {
+        return Err(ProtocolAborted::invalid_ring_pedersen_parameters(blame).into());
+    }
+
+    // common data for messages
+    tracer.stage("Compute П_mod (ψ_i)");
+    let psi = π_mod::non_interactive::prove(
+        parties_shared_state.clone(),
+        &π_mod::Data { n: N.clone() },
+        &π_mod::PrivateData {
+            p: p.clone(),
+            q: q.clone(),
+        },
+        &mut rng,
+    )
+    .map_err(Bug::PiMod)?;
+    tracer.stage("Assemble security params for П_fac (ф_i)");
+    let π_fac_security = π_fac::SecurityParams {
+        l: L::ELL,
+        epsilon: L::EPSILON,
+        q: L::q(),
+    };
+    let n_sqrt = utils::sqrt(&N);
+
+    // message to each party
+    for (j, _, d) in decommitments.iter_indexed() {
+        tracer.send_msg();
+
+        tracer.stage("Compute П_fac (ф_i^j)");
+        let phi = π_fac::prove(
+            parties_shared_state.clone(),
+            &π_fac::Aux {
+                s: d.s.clone(),
+                t: d.t.clone(),
+                rsa_modulo: d.N.clone(),
+            },
+            π_fac::Data {
+                n: &N,
+                n_root: &n_sqrt,
+            },
+            π_fac::PrivateData { p: &p, q: &q },
+            &π_fac_security,
+            &mut rng,
+        )
+        .map_err(Bug::PiFac)?;
+
+        let msg = MsgRound3 {
+            mod_proof: psi.clone(),
+            fac_proof: phi.clone(),
+        };
+        outgoings
+            .send(Outgoing::p2p(j, Msg::Round3(msg)))
+            .await
+            .map_err(IoError::send_message)?;
+        tracer.msg_sent();
+    }
+
+    // Output
+    tracer.round_begins();
+
+    tracer.receive_msgs();
+    let shares_msg_b = rounds
+        .complete(round3)
+        .await
+        .map_err(IoError::receive_message)?;
+    tracer.msgs_received();
+
+    tracer.stage("Validate ψ_j (П_mod)");
+    // verify mod proofs
+    let blame = collect_blame(
+        &decommitments,
+        &shares_msg_b,
+        |_, decommitment, proof_msg| {
+            let data = π_mod::Data {
+                n: decommitment.N.clone(),
+            };
+            let (comm, proof) = &proof_msg.mod_proof;
+            π_mod::non_interactive::verify(parties_shared_state.clone(), &data, comm, proof)
+                .is_err()
+        },
+    );
+    if !blame.is_empty() {
+        return Err(ProtocolAborted::invalid_mod_proof(blame).into());
+    }
+
+    tracer.stage("Validate ф_j (П_fac)");
+    // verify fac proofs
+    let phi_common_aux = π_fac::Aux {
+        s: s.clone(),
+        t: t.clone(),
+        rsa_modulo: N.clone(),
+    };
+    let blame = collect_blame(
+        &decommitments,
+        &shares_msg_b,
+        |_, decommitment, proof_msg| {
+            π_fac::verify(
+                parties_shared_state.clone(),
+                &phi_common_aux,
+                π_fac::Data {
+                    n: &decommitment.N,
+                    n_root: &utils::sqrt(&decommitment.N),
+                },
+                &π_fac_security,
+                &proof_msg.fac_proof,
+            )
+            .is_err()
+        },
+    );
+    if !blame.is_empty() {
+        return Err(ProtocolAborted::invalid_fac_proof(blame).into());
+    }
+
+    // verifications passed, compute final key shares
+
+    tracer.stage("Assemble auxiliary info");
+    let party_auxes = decommitments
+        .iter_including_me(&decommitment)
+        .map(|d| PartyAux {
+            N: d.N.clone(),
+            s: d.s.clone(),
+            t: d.t.clone(),
+        })
+        .collect();
+    let aux = DirtyAuxInfo {
+        p,
+        q,
+        parties: party_auxes,
+    };
+
+    tracer.protocol_ends();
+    Ok(aux.try_into().map_err(Bug::InvalidShareGenerated)?)
+}
diff --git a/cggmp21/src/key_refresh/non_threshold.rs b/cggmp21/src/key_refresh/non_threshold.rs
new file mode 100644
index 0000000..bd43bd5
--- /dev/null
+++ b/cggmp21/src/key_refresh/non_threshold.rs
@@ -0,0 +1,568 @@
+use digest::Digest;
+use futures::SinkExt;
+use generic_ec::{
+    hash_to_curve::{self, FromHash},
+    Curve, Point, Scalar, SecretScalar,
+};
+use generic_ec_zkp::{
+    hash_commitment::{self, HashCommit},
+    schnorr_pok,
+};
+use paillier_zk::{
+    libpaillier, no_small_factor::non_interactive as π_fac, paillier_blum_modulus as π_mod,
+    unknown_order::BigNumber, BigNumberExt, SafePaillierDecryptionExt, SafePaillierEncryptionExt,
+};
+use rand_core::{CryptoRng, RngCore};
+use round_based::ProtocolMessage;
+use round_based::{
+    rounds_router::{simple_store::RoundInput, RoundsRouter},
+    Delivery, Mpc, MpcParty, Outgoing,
+};
+
+use super::{Bug, KeyRefreshError, PregeneratedPrimes, ProtocolAborted};
+use crate::{
+    errors::IoError,
+    execution_id::ProtocolChoice,
+    key_share::{DirtyAuxInfo, DirtyIncompleteKeyShare, DirtyKeyShare, KeyShare, PartyAux},
+    progress::Tracer,
+    security_level::SecurityLevel,
+    utils,
+    utils::{
+        but_nth, collect_blame, collect_simple_blame, iter_peers, scalar_to_bignumber, xor_array,
+        AbortBlame,
+    },
+    zk::ring_pedersen_parameters as π_prm,
+    ExecutionId,
+};
+
+/// Message of key refresh protocol
+#[derive(ProtocolMessage, Clone)]
+// 3 kilobytes for the largest option, and 2.5 kilobytes for second largest
+#[allow(clippy::large_enum_variant)]
+pub enum Msg<E: Curve, D: Digest, L: SecurityLevel> {
+    Round1(MsgRound1<D>),
+    Round2(MsgRound2<E, D, L>),
+    Round3(MsgRound3<E>),
+}
+
+/// Message from round 1
+#[derive(Clone)]
+pub struct MsgRound1<D: Digest> {
+    pub commitment: HashCommit<D>,
+}
+/// Message from round 2
+#[derive(Clone)]
+pub struct MsgRound2<E: Curve, D: Digest, L: SecurityLevel> {
+    /// **X_i** in paper
+    pub Xs: Vec<Point<E>>,
+    /// **A_i** in paper
+    pub sch_commits_a: Vec<schnorr_pok::Commit<E>>,
+    pub N: BigNumber,
+    pub s: BigNumber,
+    pub t: BigNumber,
+    /// psi_circonflexe_i in paper
+    // this should be L::M instead, but no rustc support yet
+    pub params_proof: π_prm::Proof<{ π_prm::SECURITY }>,
+    /// rho_i in paper
+    // ideally it would be [u8; L::SECURITY_BYTES], but no rustc support yet
+    pub rho_bytes: L::Rid,
+    /// u_i in paper
+    pub decommit: hash_commitment::DecommitNonce<D>,
+}
+/// Unicast message of round 3, sent to each participant
+#[derive(Clone)]
+pub struct MsgRound3<E: Curve> {
+    /// psi_i in paper
+    // this should be L::M instead, but no rustc support yet
+    pub mod_proof: (π_mod::Commitment, π_mod::Proof<{ π_prm::SECURITY }>),
+    /// phi_i^j in paper
+    pub fac_proof: π_fac::Proof,
+    /// C_i^j in paper
+    pub C: BigNumber,
+    /// psi_i_j in paper
+    ///
+    /// Here in the paper you only send one proof, but later they require you to
+    /// verify by all the other proofs, that are never sent. We fix this here
+    /// and require each party to send every proof to everyone
+    pub sch_proofs_x: Vec<schnorr_pok::Proof<E>>,
+}
+
+pub async fn run_refresh<R, M, E, L, D>(
+    mut rng: &mut R,
+    party: M,
+    execution_id: ExecutionId<E, L, D>,
+    pregenerated: PregeneratedPrimes<L>,
+    mut tracer: Option<&mut dyn Tracer>,
+    core_share: &DirtyIncompleteKeyShare<E, L>,
+) -> Result<KeyShare<E, L>, KeyRefreshError>
+where
+    R: RngCore + CryptoRng,
+    M: Mpc<ProtocolMessage = Msg<E, D, L>>,
+    E: Curve,
+    Scalar<E>: FromHash,
+    L: SecurityLevel,
+    D: Digest<OutputSize = digest::typenum::U32> + Clone + 'static,
+{
+    tracer.protocol_begins();
+
+    tracer.stage("Retrieve auxiliary data");
+    let i = core_share.i;
+    let n = u16::try_from(core_share.public_shares.len()).map_err(|_| Bug::TooManyParties)?;
+
+    tracer.stage("Setup networking");
+    let MpcParty { delivery, .. } = party.into_party();
+    let (incomings, mut outgoings) = delivery.split();
+
+    let mut rounds = RoundsRouter::<Msg<E, D, L>>::builder();
+    let round1 = rounds.add_round(RoundInput::<MsgRound1<D>>::broadcast(i, n));
+    let round2 = rounds.add_round(RoundInput::<MsgRound2<E, D, L>>::broadcast(i, n));
+    let round3 = rounds.add_round(RoundInput::<MsgRound3<E>>::p2p(i, n));
+    let mut rounds = rounds.listen(incomings);
+
+    tracer.stage("Precompute execution id and shared state");
+    let execution_id = execution_id.evaluate(ProtocolChoice::Keygen);
+    let sid = execution_id.as_slice();
+    let tag_htc = hash_to_curve::Tag::new(&execution_id).ok_or(Bug::InvalidHashToCurveTag)?;
+    let parties_shared_state = D::new_with_prefix(execution_id);
+
+    // Round 1
+    tracer.round_begins();
+
+    tracer.stage("Retrieve primes (p and q)");
+    let PregeneratedPrimes { p, q, .. } = pregenerated;
+    tracer.stage("Compute paillier decryption key (N)");
+    let N = &p * &q;
+    let phi_N = (&p - 1) * (&q - 1);
+    let dec =
+        libpaillier::DecryptionKey::with_primes_unchecked(&p, &q).ok_or(Bug::PaillierKeyError)?;
+
+    // *x_i* in paper
+    tracer.stage("Generate secret x_i and public X_i");
+    // generate n-1 values first..
+    let mut xs = (0..n - 1)
+        .map(|_| SecretScalar::<E>::random(rng))
+        .collect::<Vec<_>>();
+    // then create a last element such that the sum is zero
+    let mut x_last = -xs.iter().sum::<Scalar<E>>();
+    xs.push(SecretScalar::new(&mut x_last));
+    debug_assert_eq!(xs.iter().sum::<Scalar<E>>(), Scalar::zero());
+    // *X_i* in paper
+    let Xs = xs
+        .iter()
+        .map(|x| Point::generator() * x)
+        .collect::<Vec<_>>();
+
+    tracer.stage("Generate auxiliary params r, λ, t, s");
+    let r = utils::sample_bigint_in_mult_group(rng, &N);
+    let lambda = BigNumber::from_rng(&phi_N, rng);
+    let t = r.modmul(&r, &N);
+    let s = t.powmod(&lambda, &N).map_err(|_| Bug::PowMod)?;
+
+    tracer.stage("Prove Πprm (ψˆ_i)");
+    let hat_psi = π_prm::prove(
+        parties_shared_state.clone(),
+        &mut rng,
+        π_prm::Data {
+            N: &N,
+            s: &s,
+            t: &t,
+        },
+        &phi_N,
+        &lambda,
+    )
+    .map_err(Bug::PiPrm)?;
+
+    tracer.stage("Compute schnorr commitment τ_j");
+    // tau_j and A_i^j in paper
+    let (taus, As) = (0..n)
+        .map(|_| schnorr_pok::prover_commits_ephemeral_secret::<E, _>(rng))
+        .unzip::<_, _, Vec<_>, Vec<_>>();
+
+    tracer.stage("Sample random bytes");
+    // rho_i in paper, this signer's share of bytes
+    let mut rho_bytes = L::Rid::default();
+    rng.fill_bytes(rho_bytes.as_mut());
+
+    tracer.stage("Compute hash commitment and sample decommitment");
+    // V_i and u_i in paper
+    // TODO: decommitment should be kappa bits
+    let (hash_commit, decommit) = HashCommit::<D>::builder()
+        .mix_bytes(sid)
+        .mix(n)
+        .mix(i)
+        .mix_many(&Xs)
+        .mix_many(As.iter().map(|a| a.0))
+        .mix_bytes(&N.to_bytes())
+        .mix_bytes(&s.to_bytes())
+        .mix_bytes(&t.to_bytes())
+        .mix_many_bytes(hat_psi.commitment.iter().map(|x| x.to_bytes()))
+        .mix_many_bytes(hat_psi.zs.iter().map(|x| x.to_bytes()))
+        .mix_bytes(&rho_bytes)
+        .commit(rng);
+
+    tracer.send_msg();
+    let commitment = MsgRound1 {
+        commitment: hash_commit,
+    };
+    outgoings
+        .send(Outgoing::broadcast(Msg::Round1(commitment.clone())))
+        .await
+        .map_err(IoError::send_message)?;
+    tracer.msg_sent();
+
+    // Round 2
+    tracer.round_begins();
+
+    tracer.receive_msgs();
+    let commitments = rounds
+        .complete(round1)
+        .await
+        .map_err(IoError::receive_message)?;
+    tracer.msgs_received();
+    tracer.send_msg();
+    let decommitment = MsgRound2 {
+        Xs: Xs.clone(),
+        sch_commits_a: As.clone(),
+        N: N.clone(),
+        s: s.clone(),
+        t: t.clone(),
+        params_proof: hat_psi,
+        rho_bytes: rho_bytes.clone(),
+        decommit,
+    };
+    outgoings
+        .send(Outgoing::broadcast(Msg::Round2(decommitment.clone())))
+        .await
+        .map_err(IoError::send_message)?;
+    tracer.msg_sent();
+
+    // Round 3
+    tracer.round_begins();
+
+    tracer.receive_msgs();
+    let decommitments = rounds
+        .complete(round2)
+        .await
+        .map_err(IoError::receive_message)?;
+    tracer.msgs_received();
+
+    // validate decommitments
+    tracer.stage("Validate round 1 decommitments");
+    let blame = collect_blame(&decommitments, &commitments, |j, decomm, comm| {
+        HashCommit::<D>::builder()
+            .mix_bytes(sid)
+            .mix(n)
+            .mix(j)
+            .mix_many(&decomm.Xs)
+            .mix_many(decomm.sch_commits_a.iter().map(|a| a.0))
+            .mix_bytes(decomm.N.to_bytes())
+            .mix_bytes(decomm.s.to_bytes())
+            .mix_bytes(decomm.t.to_bytes())
+            .mix_many_bytes(decomm.params_proof.commitment.iter().map(|x| x.to_bytes()))
+            .mix_many_bytes(decomm.params_proof.zs.iter().map(|x| x.to_bytes()))
+            .mix_bytes(&decomm.rho_bytes)
+            .verify(&comm.commitment, &decomm.decommit)
+            .is_err()
+    });
+    if !blame.is_empty() {
+        return Err(ProtocolAborted::invalid_decommitment(blame).into());
+    }
+    // Validate parties didn't skip any data
+    tracer.stage("Validate data sizes");
+    let blame = collect_simple_blame(&decommitments, |decommitment| {
+        let n = usize::from(n);
+        decommitment.Xs.len() != n || decommitment.sch_commits_a.len() != n
+    });
+    if !blame.is_empty() {
+        return Err(ProtocolAborted::invalid_data_size(blame).into());
+    }
+    // validate parameters and param_proofs
+    tracer.stage("Validate П_prm (ψ_i)");
+    let blame = collect_simple_blame(&decommitments, |d| {
+        if d.N.bit_length() < L::SECURITY_BYTES {
+            true
+        } else {
+            let data = π_prm::Data {
+                N: &d.N,
+                s: &d.s,
+                t: &d.t,
+            };
+            π_prm::verify(parties_shared_state.clone(), data, &d.params_proof).is_err()
+        }
+    });
+    if !blame.is_empty() {
+        return Err(ProtocolAborted::invalid_ring_pedersen_parameters(blame).into());
+    }
+    // validate Xs add to zero
+    tracer.stage("Validate X_i");
+    let blame = collect_simple_blame(&decommitments, |d| {
+        d.Xs.iter().sum::<Point<E>>() != Point::zero()
+    });
+    if !blame.is_empty() {
+        return Err(ProtocolAborted::invalid_x(blame).into());
+    }
+
+    tracer.stage("Compute paillier encryption keys");
+    // encryption keys for each party
+    let encs = decommitments
+        .iter()
+        .map(|d| utils::encryption_key_from_n(&d.N))
+        .collect::<Vec<_>>();
+
+    tracer.stage("Add together shared random bytes");
+    // rho in paper, collective random bytes
+    let rho_bytes = decommitments
+        .iter()
+        .map(|d| &d.rho_bytes)
+        .fold(rho_bytes, xor_array);
+
+    // common data for messages
+    tracer.stage("Compute П_mod (ψ_i)");
+    let psi = π_mod::non_interactive::prove(
+        parties_shared_state.clone(),
+        &π_mod::Data { n: N.clone() },
+        &π_mod::PrivateData {
+            p: p.clone(),
+            q: q.clone(),
+        },
+        &mut rng,
+    )
+    .map_err(Bug::PiMod)?;
+    tracer.stage("Assemble security params for П_fac (ф_i)");
+    let π_fac_security = π_fac::SecurityParams {
+        l: L::ELL,
+        epsilon: L::EPSILON,
+        q: L::q(),
+    };
+    let n_sqrt = utils::sqrt(&N);
+    tracer.stage("Compute schnorr proof ψ_i^j");
+    let challenge = Scalar::<E>::hash_concat(tag_htc, &[&i.to_be_bytes(), rho_bytes.as_ref()])
+        .map_err(Bug::HashToScalarError)?;
+    let challenge = schnorr_pok::Challenge { nonce: challenge };
+    let psis = xs
+        .iter()
+        .zip(taus.iter())
+        .map(|(x_j, secret_j)| schnorr_pok::prove(secret_j, &challenge, x_j))
+        .collect::<Vec<_>>();
+    tracer.stage("Prepare auxiliary params and security level for proofs");
+    // message to each party
+    let iterator =
+        // use every share except ours
+        but_nth(i, xs.iter())
+        .zip(&encs)
+        .zip(decommitments.iter())
+        .zip(iter_peers(i, n));
+    for (((x, enc), d), j) in iterator {
+        tracer.stage("Paillier encryption of x_i^j");
+        let (C, _) = enc
+            .encrypt_with_random(&scalar_to_bignumber(x), &mut rng)
+            .map_err(|_| Bug::PaillierEnc)?;
+        tracer.stage("Compute П_fac (ф_i^j)");
+        let phi = π_fac::prove(
+            parties_shared_state.clone(),
+            &π_fac::Aux {
+                s: d.s.clone(),
+                t: d.t.clone(),
+                rsa_modulo: d.N.clone(),
+            },
+            π_fac::Data {
+                n: &N,
+                n_root: &n_sqrt,
+            },
+            π_fac::PrivateData { p: &p, q: &q },
+            &π_fac_security,
+            &mut rng,
+        )
+        .map_err(Bug::PiFac)?;
+
+        tracer.send_msg();
+        let msg = MsgRound3 {
+            mod_proof: psi.clone(),
+            fac_proof: phi.clone(),
+            sch_proofs_x: psis.clone(),
+            C,
+        };
+        outgoings
+            .send(Outgoing::p2p(j, Msg::Round3(msg)))
+            .await
+            .map_err(IoError::send_message)?;
+        tracer.msg_sent();
+    }
+
+    // Output
+    tracer.round_begins();
+
+    tracer.receive_msgs();
+    let shares_msg_b = rounds
+        .complete(round3)
+        .await
+        .map_err(IoError::receive_message)?;
+    tracer.msgs_received();
+
+    tracer.stage("Paillier decrypt x_j^i from C_j^i");
+    // x_j^i in paper. x_i^i is a share from self to self, so it was never sent,
+    // so it's handled separately
+    let my_share = &xs[usize::from(i)];
+    // If the share couldn't be decrypted, abort with a faulty party
+    let (shares, blame) =
+        utils::partition_results(shares_msg_b.iter_indexed().map(|(j, mid, m)| {
+            let bigint = dec
+                .decrypt_to_bigint(&m.C)
+                .map_err(|_| AbortBlame::new(j, mid, mid))?;
+            Ok::<_, AbortBlame>(bigint.to_scalar())
+        }));
+    if !blame.is_empty() {
+        return Err(ProtocolAborted::paillier_dec(blame).into());
+    }
+    debug_assert_eq!(shares.len(), usize::from(n) - 1);
+
+    tracer.stage("Validate shares");
+    // verify shares are well-formed
+    let blame = shares
+        .iter()
+        .zip(decommitments.iter_indexed())
+        .filter_map(|(share, (j, msg_id, decommitment))| {
+            let i = usize::from(i);
+            let X = Point::generator() * share;
+            if X != decommitment.Xs[i] {
+                Some(AbortBlame::new(j, msg_id, msg_id))
+            } else {
+                None
+            }
+        })
+        .collect::<Vec<_>>();
+    if !blame.is_empty() {
+        return Err(ProtocolAborted::invalid_x_share(blame).into());
+    }
+    // It is possible at this point to report a bad party to others, but we
+    // don't implement it now
+
+    tracer.stage("Validate schnorr proofs п_j and ψ_j^k");
+    // verify sch proofs for x
+    let blame = utils::try_collect_blame(
+        &decommitments,
+        &shares_msg_b,
+        |j, decommitment, proof_msg| {
+            let challenge =
+                Scalar::<E>::hash_concat(tag_htc, &[&j.to_be_bytes(), rho_bytes.as_ref()])
+                    .map_err(Bug::HashToScalarError)?;
+            let challenge = schnorr_pok::Challenge { nonce: challenge };
+
+            // x length is verified above
+            if proof_msg.sch_proofs_x.len() != decommitment.Xs.len() {
+                return Ok(true);
+            }
+            // proof for x, i.e. psi_j^k for every k
+            let iterator = proof_msg
+                .sch_proofs_x
+                .iter()
+                .zip(&decommitment.Xs)
+                .zip(&decommitment.sch_commits_a);
+            for ((sch_proof, x), commit) in iterator {
+                if sch_proof.verify(commit, &challenge, x).is_err() {
+                    return Ok(true);
+                }
+            }
+            // explicit type ascription because it can't get inferred
+            Ok::<_, Bug>(false)
+        },
+    )?;
+    if !blame.is_empty() {
+        return Err(ProtocolAborted::invalid_schnorr_proof(blame).into());
+    }
+
+    tracer.stage("Validate ψ_j (П_mod)");
+    // verify mod proofs
+    let blame = collect_blame(
+        &decommitments,
+        &shares_msg_b,
+        |_, decommitment, proof_msg| {
+            let data = π_mod::Data {
+                n: decommitment.N.clone(),
+            };
+            let (comm, proof) = &proof_msg.mod_proof;
+            π_mod::non_interactive::verify(parties_shared_state.clone(), &data, comm, proof)
+                .is_err()
+        },
+    );
+    if !blame.is_empty() {
+        return Err(ProtocolAborted::invalid_mod_proof(blame).into());
+    }
+
+    tracer.stage("Validate ф_j (П_fac)");
+    // verify fac proofs
+    let phi_common_aux = π_fac::Aux {
+        s: s.clone(),
+        t: t.clone(),
+        rsa_modulo: N.clone(),
+    };
+    let blame = collect_blame(
+        &decommitments,
+        &shares_msg_b,
+        |_, decommitment, proof_msg| {
+            π_fac::verify(
+                parties_shared_state.clone(),
+                &phi_common_aux,
+                π_fac::Data {
+                    n: &decommitment.N,
+                    n_root: &utils::sqrt(&decommitment.N),
+                },
+                &π_fac_security,
+                &proof_msg.fac_proof,
+            )
+            .is_err()
+        },
+    );
+    if !blame.is_empty() {
+        return Err(ProtocolAborted::invalid_fac_proof(blame).into());
+    }
+
+    // verifications passed, compute final key shares
+
+    let old_core_share = core_share.clone();
+    tracer.stage("Calculate new x_i");
+    let x_sum = shares.iter().sum::<Scalar<E>>() + my_share;
+    let mut x_star = old_core_share.x + x_sum;
+    tracer.stage("Calculate new X_i");
+    let X_sums = (0..n).map(|k| {
+        let k = usize::from(k);
+        decommitments
+            .iter_including_me(&decommitment)
+            .map(|d| d.Xs[k])
+            .sum::<Point<E>>()
+    });
+    let X_stars = old_core_share
+        .public_shares
+        .into_iter()
+        .zip(X_sums)
+        .map(|(x, p)| x + p)
+        .collect();
+
+    tracer.stage("Assemble new core share");
+    let new_core_share = DirtyIncompleteKeyShare {
+        public_shares: X_stars,
+        x: SecretScalar::new(&mut x_star),
+        ..old_core_share
+    };
+    tracer.stage("Assemble auxiliary info");
+    let party_auxes = decommitments
+        .iter_including_me(&decommitment)
+        .map(|d| PartyAux {
+            N: d.N.clone(),
+            s: d.s.clone(),
+            t: d.t.clone(),
+        })
+        .collect();
+    let aux = DirtyAuxInfo {
+        p,
+        q,
+        parties: party_auxes,
+    };
+    let key_share = DirtyKeyShare {
+        core: new_core_share,
+        aux,
+    };
+
+    tracer.protocol_ends();
+    Ok(key_share.try_into().map_err(Bug::InvalidShareGenerated)?)
+}
diff --git a/cggmp21/src/key_share.rs b/cggmp21/src/key_share.rs
index 9cca173..632e894 100644
--- a/cggmp21/src/key_share.rs
+++ b/cggmp21/src/key_share.rs
@@ -28,6 +28,8 @@ pub type KeyShare<E, L> = Valid<DirtyKeyShare<E, L>>;
 #[doc = include_str!("../docs/validated_key_share_note.md")]
 pub type IncompleteKeyShare<E, L> = Valid<DirtyIncompleteKeyShare<E, L>>;
 
+pub type AuxInfo = Valid<DirtyAuxInfo>;
+
 /// Dirty (unvalidated) incomplete key share
 ///
 #[doc = include_str!("../docs/incomplete_key_share.md")]
@@ -57,15 +59,10 @@ pub struct DirtyIncompleteKeyShare<E: Curve, L: SecurityLevel> {
     pub x: SecretScalar<E>,
 }
 
-/// Dirty (unvalidated) key share
-///
-#[doc = include_str!("../docs/key_share.md")]
-#[serde_as]
+/// Dirty aux info
 #[derive(Clone, Serialize, Deserialize)]
 #[serde(bound = "")]
-pub struct DirtyKeyShare<E: Curve, L: SecurityLevel> {
-    /// Core key share
-    pub core: DirtyIncompleteKeyShare<E, L>,
+pub struct DirtyAuxInfo {
     /// Secret prime $p$
     pub p: BigNumber,
     /// Secret prime $q$
@@ -76,8 +73,19 @@ pub struct DirtyKeyShare<E: Curve, L: SecurityLevel> {
     pub parties: Vec<PartyAux>,
 }
 
+/// Dirty (unvalidated) key share
+///
+#[doc = include_str!("../docs/key_share.md")]
+#[derive(Clone, Serialize, Deserialize)]
+#[serde(bound = "")]
+pub struct DirtyKeyShare<E: Curve, L: SecurityLevel> {
+    /// Core key share
+    pub core: DirtyIncompleteKeyShare<E, L>,
+    /// Auxiliary info
+    pub aux: DirtyAuxInfo,
+}
+
 /// Party public auxiliary data
-#[serde_as]
 #[derive(Debug, Clone, Serialize, Deserialize)]
 #[serde(bound = "")]
 pub struct PartyAux {
@@ -191,22 +199,10 @@ impl<E: Curve, L: SecurityLevel> DirtyIncompleteKeyShare<E, L> {
     }
 }
 
-impl<E: Curve, L: SecurityLevel> DirtyKeyShare<E, L> {
-    /// Validates a share
-    ///
-    /// Performs consistency checks against a key share, returns `Ok(())` if share looks OK.
+impl DirtyAuxInfo {
+    /// Performs consistency checks against aux info, returns a valid share
+    /// you can use with other algorithms
     pub fn validate(&self) -> Result<(), InvalidKeyShare> {
-        self.core.validate()?;
-
-        if self.core.public_shares.len() != self.parties.len() {
-            return Err(InvalidKeyShareReason::AuxLen.into());
-        }
-
-        let N_i = &self.parties[usize::from(self.core.i)].N;
-        if *N_i != &self.p * &self.q {
-            return Err(InvalidKeyShareReason::PrimesMul.into());
-        }
-
         if self
             .parties
             .iter()
@@ -219,6 +215,55 @@ impl<E: Curve, L: SecurityLevel> DirtyKeyShare<E, L> {
     }
 }
 
+impl<E: Curve, L: SecurityLevel> DirtyKeyShare<E, L> {
+    /// Perform consistency check between core and aux
+    fn validate_consistency(&self) -> Result<(), InvalidKeyShare> {
+        if self.core.public_shares.len() != self.aux.parties.len() {
+            return Err(InvalidKeyShareReason::AuxLen.into());
+        }
+
+        let N_i = &self.aux.parties[usize::from(self.core.i)].N;
+        if *N_i != &self.aux.p * &self.aux.q {
+            return Err(InvalidKeyShareReason::PrimesMul.into());
+        }
+
+        Ok(())
+    }
+
+    /// Validates a share
+    ///
+    /// Performs consistency checks against a key share, returns `Ok(())` if share looks OK.
+    pub fn validate(&self) -> Result<(), InvalidKeyShare> {
+        self.core.validate()?;
+        self.aux.validate()?;
+        self.validate_consistency()
+    }
+}
+
+impl<E: Curve, L: SecurityLevel> KeyShare<E, L> {
+    /// Make key share from valid components, only checking for consistency
+    /// between them
+    pub fn make(core: IncompleteKeyShare<E, L>, aux: AuxInfo) -> Result<Self, InvalidKeyShare> {
+        let r = DirtyKeyShare {
+            core: core.0,
+            aux: aux.0,
+        };
+        r.validate_consistency()?;
+        Ok(Valid(r))
+    }
+
+    /// Update aux info of a valid key share. Checks that the new aux info is
+    /// consistent with key share
+    pub fn update_aux(self, aux: AuxInfo) -> Result<Self, InvalidKeyShare> {
+        let r = DirtyKeyShare {
+            core: self.0.core,
+            aux: aux.0,
+        };
+        r.validate_consistency()?;
+        Ok(Valid(r))
+    }
+}
+
 impl<E: Curve, L: SecurityLevel> AsRef<DirtyIncompleteKeyShare<E, L>> for DirtyKeyShare<E, L> {
     fn as_ref(&self) -> &DirtyIncompleteKeyShare<E, L> {
         &self.core
@@ -403,6 +448,14 @@ impl<E: Curve, L: SecurityLevel> TryFrom<DirtyIncompleteKeyShare<E, L>>
     }
 }
 
+impl TryFrom<DirtyAuxInfo> for AuxInfo {
+    type Error = InvalidKeyShare;
+    fn try_from(value: DirtyAuxInfo) -> Result<Self, Self::Error> {
+        value.validate()?;
+        Ok(Self(value))
+    }
+}
+
 impl<E: Curve, L: SecurityLevel> TryFrom<DirtyKeyShare<E, L>> for KeyShare<E, L> {
     type Error = InvalidKeyShare;
     fn try_from(key_share: DirtyKeyShare<E, L>) -> Result<Self, Self::Error> {
diff --git a/cggmp21/src/keygen.rs b/cggmp21/src/keygen.rs
index 675766a..ec37148 100644
--- a/cggmp21/src/keygen.rs
+++ b/cggmp21/src/keygen.rs
@@ -64,6 +64,7 @@ where
     L: SecurityLevel,
     D: Digest + Clone + 'static,
 {
+    /// Specifies to generate key shares for a threshold scheme
     pub fn set_threshold(self, t: u16) -> GenericKeygenBuilder<E, L, D, WithThreshold> {
         GenericKeygenBuilder {
             i: self.i,
diff --git a/cggmp21/src/lib.rs b/cggmp21/src/lib.rs
index 58eca7d..b6e9d73 100644
--- a/cggmp21/src/lib.rs
+++ b/cggmp21/src/lib.rs
@@ -13,7 +13,7 @@ pub use {
 };
 
 use generic_ec::{coords::HasAffineX, hash_to_curve::FromHash, Curve, Point, Scalar};
-use key_share::{AnyKeyShare, IncompleteKeyShare, KeyShare};
+use key_share::{AnyKeyShare, KeyShare};
 use round_based::PartyIndex;
 use security_level::SecurityLevel;
 use sha2::Sha256;
@@ -54,22 +54,25 @@ where
     keygen::KeygenBuilder::new(i, n)
 }
 
-/// Protocol for finalizing the keygen by generating aux info and performing
-/// initial key refresh.
+/// Protocol for finalizing the keygen by generating aux info.
 ///
 /// PregeneratedPrimes can be obtained with [`key_refresh::PregeneratedPrimes::generate`]
-pub fn aux_info_gen<E, L>(
-    core_share: &IncompleteKeyShare<E, L>,
+pub fn aux_info_gen<'a, E, L>(
+    t: u16,
+    n: u16,
     pregenerated: key_refresh::PregeneratedPrimes<L>,
-) -> key_refresh::KeyRefreshBuilder<E, L, Sha256>
+) -> key_refresh::AuxInfoGenerationBuilder<'a, E, L, Sha256>
 where
     E: Curve,
     L: SecurityLevel,
 {
-    key_refresh::KeyRefreshBuilder::new(core_share, pregenerated)
+    key_refresh::GenericKeyRefreshBuilder::new_aux_gen(t, n, pregenerated)
 }
 
-/// Protocol for performing key refresh
+/// Protocol for performing key refresh. Can be used to perform initial refresh
+/// with aux info generation, or for a refersh of a complete keyshare.
+///
+/// Doesn't work with threshold key shares at this point.
 ///
 /// PregeneratedPrimes can be obtained with [`key_refresh::PregeneratedPrimes::generate`]
 pub fn key_refresh<E, L>(
diff --git a/cggmp21/src/signing.rs b/cggmp21/src/signing.rs
index 8b3ceb1..5d75979 100644
--- a/cggmp21/src/signing.rs
+++ b/cggmp21/src/signing.rs
@@ -334,6 +334,7 @@ where
 
     // Validate arguments
     let n: u16 = key_share
+        .aux
         .parties
         .len()
         .try_into()
@@ -381,8 +382,8 @@ where
     debug_assert_eq!(key_share.core.shared_public_key, X.iter().sum::<Point<E>>());
 
     // Assemble rest of the data
-    let (p_i, q_i) = (&key_share.p, &key_share.q);
-    let R = subset(S, &key_share.parties).ok_or(Bug::Subset)?;
+    let (p_i, q_i) = (&key_share.aux.p, &key_share.aux.q);
+    let R = subset(S, &key_share.aux.parties).ok_or(Bug::Subset)?;
 
     // t-out-of-t signing
     signing_n_out_of_n(
diff --git a/cggmp21/src/trusted_dealer.rs b/cggmp21/src/trusted_dealer.rs
index e752fab..45d1c5c 100644
--- a/cggmp21/src/trusted_dealer.rs
+++ b/cggmp21/src/trusted_dealer.rs
@@ -9,7 +9,8 @@ use generic_ec::{Curve, NonZero, Point, Scalar, SecretScalar};
 
 use crate::{
     key_share::{
-        DirtyIncompleteKeyShare, DirtyKeyShare, InvalidKeyShare, KeyShare, PartyAux, VssSetup,
+        DirtyAuxInfo, DirtyIncompleteKeyShare, DirtyKeyShare, InvalidKeyShare, KeyShare, PartyAux,
+        VssSetup,
     },
     security_level::SecurityLevel,
     utils::sample_bigint_in_mult_group,
@@ -91,10 +92,12 @@ pub fn mock_keygen<E: Curve, L: SecurityLevel, R: RngCore + CryptoRng>(
         .zip(primes_setups)
         .map(|(core_share, primes_setup)| {
             DirtyKeyShare {
-                p: primes_setup.p,
-                q: primes_setup.q,
-                parties: parties_aux.clone(),
                 core: core_share,
+                aux: DirtyAuxInfo {
+                    p: primes_setup.p,
+                    q: primes_setup.q,
+                    parties: parties_aux.clone(),
+                },
             }
             .try_into()
         })
diff --git a/test-data/precomputed_shares.json b/test-data/precomputed_shares.json
index a655116..efadb6d 100644
--- a/test-data/precomputed_shares.json
+++ b/test-data/precomputed_shares.json
@@ -1,3579 +1,3315 @@
 {
   "t=None,n=10,curve=secp256k1": [
     {
+      "aux": {
+        "p": "d61ddba8d66fd0975b616ff4f936d049b29ba08775827b69c4fcabe45862cea21f16261624295c9ca8bb24f04d6d2704fbebfa7d9cf8c37961d84acf1809ae3e09c2e92a02d6498a358c1faba395560913ced56e659d00fb4f0dd4b470dc721062cd26560272ad0fd8423aa8f9ad736de1aea4974d26f1cfd5f1ea302d181c0b",
+        "parties": [
+          {
+            "N": "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",
+            "s": "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",
+            "t": "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"
+          },
+          {
+            "N": "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",
+            "s": "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",
+            "t": "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"
+          },
+          {
+            "N": "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",
+            "s": "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",
+            "t": "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"
+          },
+          {
+            "N": "979bac04764fda0d47092c93c9da9247ab89c08ec088019f4dc04bc4e8564e9627d8d9a168efcbf718a76b2b7c827a38fdacc4373be33ebac205063c4672593c91e7b98815c8c2a6fe3b4fbb2bc15699d3e40cdafb62ac2c31bf1467acc9f26027ecdb2b498a97749e1c356d880454ad3a5989ca9c20e770489b7ecd6695487bf3126752091891db63c03fe8fc4d791ccc746c907ec6198a348c6173fcc4794c5f10b131b2ce6132fcdb7d55bf7f8d2abfdebe304de3355d577d7c93443365b737a3edb3228f5a7cf2bb263a2e0557180906183865214d56247322ede09c11fb77a59ccaf0203b9ea7ccd430c9bcc387c3f15fcd8d1c78c04f9e8e988cc62ded",
+            "s": "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",
+            "t": "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"
+          },
+          {
+            "N": "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",
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+          },
+          {
+            "N": "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",
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+          },
+          {
+            "N": "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",
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+            "t": "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"
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+          {
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       "core": {
         "curve": "secp256k1",
         "i": 5,
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       "core": {
         "curve": "secp256k1",
         "i": 9,
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         "curve": "secp256r1",
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       "core": {
         "curve": "secp256r1",
         "i": 3,
         "public_shares": [
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         "curve": "secp256r1",
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   "t=None,n=2,curve=secp256k1": [
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     }
   ],
   "t=None,n=5,curve=secp256k1": [
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   ],
   "t=None,n=7,curve=secp256k1": [
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         "curve": "secp256k1",
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   "t=Some(2),n=10,curve=secp256k1": [
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@@ -3619,92 +3355,83 @@
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@@ -3750,92 +3477,83 @@
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       "core": {
         "curve": "secp256k1",
         "i": 2,
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@@ -3881,92 +3599,83 @@
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       "core": {
         "curve": "secp256k1",
         "i": 3,
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         "vss_setup": {
           "I": [
             {
@@ -4012,92 +3721,83 @@
           ],
           "min_signers": 2
         },
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         "vss_setup": {
           "I": [
             {
@@ -4143,92 +3843,83 @@
           ],
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@@ -4274,92 +3965,83 @@
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             {
@@ -4405,92 +4087,83 @@
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       "core": {
         "curve": "secp256k1",
         "i": 7,
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@@ -4536,92 +4209,83 @@
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       "core": {
         "curve": "secp256k1",
         "i": 8,
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         "vss_setup": {
           "I": [
             {
@@ -4667,92 +4331,83 @@
           ],
           "min_signers": 2
         },
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         "curve": "secp256k1",
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         "vss_setup": {
           "I": [
             {
@@ -4798,94 +4453,85 @@
           ],
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   "t=Some(2),n=10,curve=secp256r1": [
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@@ -4931,92 +4577,83 @@
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       "core": {
         "curve": "secp256r1",
         "i": 1,
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@@ -5062,92 +4699,83 @@
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       "core": {
         "curve": "secp256r1",
         "i": 2,
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-        "shared_public_key": "035c2d53ecfe807f73c613f644a6b4c54173d2113baa38a3c50c0fb1be697fa71c",
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+        ],
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+        "shared_public_key": "02ba79a28e00b786aa8988cf1aac227037521c94583a4fcae4de304207ddac7cd4",
         "vss_setup": {
           "I": [
             {
@@ -5193,92 +4821,83 @@
           ],
           "min_signers": 2
         },
-        "x": "c4ecd7d5cfe1dea11a5acfa323b223045df91d68c57be9a031bd88cbce73bef9"
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-      "parties": [
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-        "shared_public_key": "035c2d53ecfe807f73c613f644a6b4c54173d2113baa38a3c50c0fb1be697fa71c",
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         "vss_setup": {
           "I": [
             {
@@ -5324,92 +4943,83 @@
           ],
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         "vss_setup": {
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             {
@@ -5455,92 +5065,83 @@
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       "core": {
         "curve": "secp256r1",
         "i": 5,
         "public_shares": [
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@@ -5586,92 +5187,83 @@
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       "core": {
         "curve": "secp256r1",
         "i": 6,
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-        "shared_public_key": "035c2d53ecfe807f73c613f644a6b4c54173d2113baa38a3c50c0fb1be697fa71c",
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+        "shared_public_key": "02ba79a28e00b786aa8988cf1aac227037521c94583a4fcae4de304207ddac7cd4",
         "vss_setup": {
           "I": [
             {
@@ -5717,92 +5309,83 @@
           ],
           "min_signers": 2
         },
-        "x": "76360b9cf75c35ffb90ec72e0836055df8bd9632a11f4c01b2be9f253d5f58d3"
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-      "parties": [
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         "curve": "secp256r1",
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         "vss_setup": {
           "I": [
             {
@@ -5848,92 +5431,83 @@
           ],
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         "vss_setup": {
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             {
@@ -5979,92 +5553,83 @@
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       "core": {
         "curve": "secp256r1",
         "i": 9,
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@@ -6110,86 +5675,37 @@
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+      }
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   ],
   "t=Some(2),n=2,curve=secp256k1": [
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+      },
       "core": {
         "curve": "secp256k1",
         "i": 0,
         "public_shares": [
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-          "0376a49e9ac87cb8f39c9d3d0e9a207b5fc279820238c84b5729dc69cb45ddabbd"
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-        "rid": "c7322fe7c6c98d3c8bddfcdfc6c22bbbe076f490f90cb7f6f73019947c408559",
-        "shared_public_key": "025f1b3183e1fd224f2d56a83ea1a3da5818a4da5c1bd7ba26a66dcbe7f3778e21",
+        "rid": "9b1ead6d6b9a50c91b21958bc54ff447feec6aafe41508a187fd844367e8cdff",
+        "shared_public_key": "02ca12102744070501ebb92364595f84445a260fc0c1a83a9bf4a6822322398e53",
         "vss_setup": {
           "I": [
             {
@@ -6203,36 +5719,35 @@
           ],
           "min_signers": 2
         },
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+      }
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       "core": {
         "curve": "secp256k1",
         "i": 1,
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-          "0376a49e9ac87cb8f39c9d3d0e9a207b5fc279820238c84b5729dc69cb45ddabbd"
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-        "rid": "c7322fe7c6c98d3c8bddfcdfc6c22bbbe076f490f90cb7f6f73019947c408559",
-        "shared_public_key": "025f1b3183e1fd224f2d56a83ea1a3da5818a4da5c1bd7ba26a66dcbe7f3778e21",
+        "rid": "9b1ead6d6b9a50c91b21958bc54ff447feec6aafe41508a187fd844367e8cdff",
+        "shared_public_key": "02ca12102744070501ebb92364595f84445a260fc0c1a83a9bf4a6822322398e53",
         "vss_setup": {
           "I": [
             {
@@ -6246,38 +5761,37 @@
           ],
           "min_signers": 2
         },
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+      }
     }
   ],
   "t=Some(2),n=2,curve=secp256r1": [
     {
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+          }
+        ],
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+      },
       "core": {
         "curve": "secp256r1",
         "i": 0,
         "public_shares": [
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-          "03da38b87568e5889d66427c80cda0c0507aa4938337ec74569a65c5f88a2ee95d"
+          "026046649756a555ed13d227a7467f5239811396f4ff88dec6d3b979fc2437c819",
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-        "rid": "5b08e749fcca63d6666d3ac31a19e909d91f27b9b7d8ed5a5dfcf9e8865f8d27",
-        "shared_public_key": "021404212d2bc44b450eecd662bd8bd180d524a9c2b5cf283bdf25f912184534ce",
+        "rid": "2db677acbad9609f9bd317ba486777dc210a9a0273ffc138215197bc1c951a6c",
+        "shared_public_key": "0366368f87521f91b63a1921294bac5514cea6c6161e6b10d87f85d3e1b1807e44",
         "vss_setup": {
           "I": [
             {
@@ -6291,36 +5805,35 @@
           ],
           "min_signers": 2
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+      }
     },
     {
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+      },
       "core": {
         "curve": "secp256r1",
         "i": 1,
         "public_shares": [
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-          "03da38b87568e5889d66427c80cda0c0507aa4938337ec74569a65c5f88a2ee95d"
+          "026046649756a555ed13d227a7467f5239811396f4ff88dec6d3b979fc2437c819",
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-        "rid": "5b08e749fcca63d6666d3ac31a19e909d91f27b9b7d8ed5a5dfcf9e8865f8d27",
-        "shared_public_key": "021404212d2bc44b450eecd662bd8bd180d524a9c2b5cf283bdf25f912184534ce",
+        "rid": "2db677acbad9609f9bd317ba486777dc210a9a0273ffc138215197bc1c951a6c",
+        "shared_public_key": "0366368f87521f91b63a1921294bac5514cea6c6161e6b10d87f85d3e1b1807e44",
         "vss_setup": {
           "I": [
             {
@@ -6334,39 +5847,43 @@
           ],
           "min_signers": 2
         },
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     }
   ],
   "t=Some(2),n=3,curve=secp256k1": [
     {
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+      },
       "core": {
         "curve": "secp256k1",
         "i": 0,
         "public_shares": [
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-          "031933584d08956dc4b74a1d3e5a5d4dfa08d82d48c4dee2e138fb496eca7a9137",
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-        "shared_public_key": "03ae5f3bae2b8ca2e975f2c37c8df7a3759aa2659337990d409c48ebb5ff726d8d",
+        "rid": "f2eb8fd861fed8ddac13c2025849b3b645a964507d81f3a07fa14a576f04beae",
+        "shared_public_key": "0214ab7bdc99e1708e342b31da79a6e13ddce94cee94b83c617d4b5d6f41c23367",
         "vss_setup": {
           "I": [
             {
@@ -6384,43 +5901,41 @@
           ],
           "min_signers": 2
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         "curve": "secp256k1",
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-        "shared_public_key": "03ae5f3bae2b8ca2e975f2c37c8df7a3759aa2659337990d409c48ebb5ff726d8d",
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         "vss_setup": {
           "I": [
             {
@@ -6438,43 +5953,41 @@
           ],
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-        "shared_public_key": "03ae5f3bae2b8ca2e975f2c37c8df7a3759aa2659337990d409c48ebb5ff726d8d",
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             {
@@ -6492,45 +6005,43 @@
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   ],
   "t=Some(2),n=3,curve=secp256r1": [
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-        "shared_public_key": "038c5cb7ff2a7076e9ef36416f1f0c0caaad5dc640486f3ac1dc806c04b98b2a07",
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         "vss_setup": {
           "I": [
             {
@@ -6548,43 +6059,41 @@
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-        "shared_public_key": "038c5cb7ff2a7076e9ef36416f1f0c0caaad5dc640486f3ac1dc806c04b98b2a07",
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         "vss_setup": {
           "I": [
             {
@@ -6602,43 +6111,41 @@
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-        "shared_public_key": "038c5cb7ff2a7076e9ef36416f1f0c0caaad5dc640486f3ac1dc806c04b98b2a07",
+        "rid": "9318e4f7b66a6cc2aeb916af0bed229128b1a986ce9a7d60d5118bf0df707462",
+        "shared_public_key": "03eea0a13fbd6920a42ca8a80dc884faf99b92ff81200d6d335822ad05f16b8546",
         "vss_setup": {
           "I": [
             {
@@ -6656,47 +6163,55 @@
           ],
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   ],
   "t=Some(2),n=5,curve=secp256k1": [
     {
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           "I": [
             {
@@ -6722,57 +6237,53 @@
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+          }
+        ],
+        "q": "dde6a969c8c9d5de1d5909a3614a079e1ea3f02f792deefebdff1dfbeb6d365ef6efc8821c17f51e339c2698b91f57a3d88ce23ed63d2714601b377888b7bc539e725a51d5164616325ddc37a6a87f9fbbd896f480fb608225792c3190ab747f09d4ea8e7a509bd1074a9b049d56403c4470a125f8de59a71e76392a05aa44f3"
+      },
       "core": {
         "curve": "secp256k1",
         "i": 1,
         "public_shares": [
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-          "03d4d6bfe84d9ed5323d5041620cd074cd64558755ce1f201ba06abdb8b8c0a5b4",
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-          "02d1ea59ff513d9f5456120e48d01c19d1a566cbad32de2a0ab664a4cbd209e5a3"
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-        "rid": "02d4390ed1ee11c9a3def619d018a03864bb5e0274ede4c90ec405134968ab20",
-        "shared_public_key": "0256780ce07ee16b512c448307e007b4739a3758351b35163087b351a749bbf5b2",
+          "03a5568960054c0fd45fa985e5165419c7591e1f9c066daf2d27f6eac8f0eaeb93",
+          "034a2173ab5485d74ace95397593e1327e6d2d5f142381e56ad00e274f2a80fc2b",
+          "037ddff1fa216f980d6afd95acb56b2297b173a00ed0eb0d02e8aeeefa085b930b",
+          "03ce428190a03ce839931ae74223e46570d7cc92b15474b761c2624f2c0d3edafd",
+          "03f01dcc47bc42528c27561cefdc9967506d5a9c95ea3869719f878ab744545d06"
+        ],
+        "rid": "c2e27d89eafb6bf5ea2d2d11bf717dc34d35ecddff9d2444e29deec10db22a10",
+        "shared_public_key": "02cf13ea293e1a37d0b70d96b6471041a7556ec096424d9cf197be0ec3b8820913",
         "vss_setup": {
           "I": [
             {
@@ -6798,57 +6309,53 @@
           ],
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         "curve": "secp256k1",
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         "vss_setup": {
           "I": [
             {
@@ -6874,57 +6381,53 @@
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       "core": {
         "curve": "secp256k1",
         "i": 3,
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-        "shared_public_key": "0256780ce07ee16b512c448307e007b4739a3758351b35163087b351a749bbf5b2",
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         "vss_setup": {
           "I": [
             {
@@ -6950,57 +6453,53 @@
           ],
           "min_signers": 2
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           "I": [
             {
@@ -7026,59 +6525,55 @@
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     }
   ],
   "t=Some(2),n=5,curve=secp256r1": [
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       "core": {
         "curve": "secp256r1",
         "i": 0,
         "public_shares": [
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-        "shared_public_key": "038bc1885a6c73025b05b0b58cd1cc594e0765dedef56aeb35ca98c75f4a61f0ca",
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         "vss_setup": {
           "I": [
             {
@@ -7104,57 +6599,53 @@
           ],
           "min_signers": 2
         },
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         "curve": "secp256r1",
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         "vss_setup": {
           "I": [
             {
@@ -7180,57 +6671,53 @@
           ],
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       "core": {
         "curve": "secp256r1",
         "i": 2,
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-        "shared_public_key": "038bc1885a6c73025b05b0b58cd1cc594e0765dedef56aeb35ca98c75f4a61f0ca",
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         "vss_setup": {
           "I": [
             {
@@ -7256,57 +6743,53 @@
           ],
           "min_signers": 2
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           "I": [
             {
@@ -7332,57 +6815,53 @@
           ],
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         "curve": "secp256r1",
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         "vss_setup": {
           "I": [
             {
@@ -7408,61 +6887,67 @@
           ],
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@@ -7496,71 +6981,65 @@
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             {
@@ -7594,71 +7073,65 @@
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             {
@@ -7692,71 +7165,65 @@
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             {
@@ -7790,71 +7257,65 @@
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             {
@@ -7888,71 +7349,65 @@
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             {
@@ -7986,71 +7441,65 @@
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             {
@@ -8084,73 +7533,67 @@
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@@ -8184,71 +7627,65 @@
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         "vss_setup": {
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             {
@@ -8282,71 +7719,65 @@
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         "vss_setup": {
           "I": [
             {
@@ -8380,71 +7811,65 @@
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         "vss_setup": {
           "I": [
             {
@@ -8478,71 +7903,65 @@
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         "vss_setup": {
           "I": [
             {
@@ -8576,71 +7995,65 @@
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         "vss_setup": {
           "I": [
             {
@@ -8674,71 +8087,65 @@
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           "I": [
             {
@@ -8772,76 +8179,85 @@
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         "vss_setup": {
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             {
@@ -8887,92 +8303,83 @@
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         "vss_setup": {
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             {
@@ -9018,92 +8425,83 @@
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             {
@@ -9149,92 +8547,83 @@
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       "core": {
         "curve": "secp256k1",
         "i": 3,
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@@ -9280,92 +8669,83 @@
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         "curve": "secp256k1",
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         "vss_setup": {
           "I": [
             {
@@ -9411,92 +8791,83 @@
           ],
           "min_signers": 3
         },
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         "vss_setup": {
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@@ -9542,92 +8913,83 @@
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         "vss_setup": {
           "I": [
             {
@@ -9673,92 +9035,83 @@
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       "core": {
         "curve": "secp256k1",
         "i": 7,
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@@ -9804,92 +9157,83 @@
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       "core": {
         "curve": "secp256k1",
         "i": 8,
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         "vss_setup": {
           "I": [
             {
@@ -9933,94 +9277,85 @@
               "scalar": "000000000000000000000000000000000000000000000000000000000000000a"
             }
           ],
-          "min_signers": 3
-        },
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             {
@@ -10066,94 +9401,85 @@
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   "t=Some(3),n=10,curve=secp256r1": [
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@@ -10199,92 +9525,83 @@
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       "core": {
         "curve": "secp256r1",
         "i": 1,
         "public_shares": [
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@@ -10330,92 +9647,83 @@
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+      },
       "core": {
         "curve": "secp256r1",
         "i": 2,
         "public_shares": [
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-        "shared_public_key": "03d7867f6d02a7ef191c1c04f5db5b49a8caed3319a0a69d940bb28630dc40fa4d",
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+          "03bd26ab5533153cd6213eb1c9f743ca97660c477858ef8105523a25decce24ee6"
+        ],
+        "rid": "d77e85bf5791437156513bc54e2a72dc472dd7afb5bcaf18aa70bee557af4aa7",
+        "shared_public_key": "0281151a728aaa3b7eb18b7a9faa24edb8af2b7844b89dbb56c84b639080cee3ef",
         "vss_setup": {
           "I": [
             {
@@ -10461,92 +9769,83 @@
           ],
           "min_signers": 3
         },
-        "x": "e5ae16302e3f7bbf7135feb166eb33d902ce4f8daa67938903610dfaae03ae1d"
-      },
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-      "parties": [
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         "vss_setup": {
           "I": [
             {
@@ -10592,92 +9891,83 @@
           ],
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         "vss_setup": {
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             {
@@ -10723,92 +10013,83 @@
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       "core": {
         "curve": "secp256r1",
         "i": 5,
         "public_shares": [
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@@ -10854,92 +10135,83 @@
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+      },
       "core": {
         "curve": "secp256r1",
         "i": 6,
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-        "shared_public_key": "03d7867f6d02a7ef191c1c04f5db5b49a8caed3319a0a69d940bb28630dc40fa4d",
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+          "03bd26ab5533153cd6213eb1c9f743ca97660c477858ef8105523a25decce24ee6"
+        ],
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+        "shared_public_key": "0281151a728aaa3b7eb18b7a9faa24edb8af2b7844b89dbb56c84b639080cee3ef",
         "vss_setup": {
           "I": [
             {
@@ -10985,92 +10257,83 @@
           ],
           "min_signers": 3
         },
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             {
@@ -11116,92 +10379,83 @@
           ],
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             {
@@ -11247,92 +10501,83 @@
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       "core": {
         "curve": "secp256r1",
         "i": 9,
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@@ -11378,87 +10623,43 @@
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   "t=Some(3),n=3,curve=secp256k1": [
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       "core": {
         "curve": "secp256k1",
         "i": 0,
         "public_shares": [
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-          "02c84d5d4b728470f8d83728aae31f1029a375953fd414b83da7b30fbf695c770a",
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-        "shared_public_key": "03b61a18df2143a1e5514d1dc6ca9c607bd99cd4e769374e9dc8efece7f4eca56c",
+        "rid": "8cf312dae70d8169c4228ff933a1578c395403113277927e2bc2eb9e49bee07e",
+        "shared_public_key": "0328c282687abecbc54e80e6e4ef457d85ccbd5ed6d15b497beb7787a98de66c35",
         "vss_setup": {
           "I": [
             {
@@ -11476,43 +10677,41 @@
           ],
           "min_signers": 3
         },
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         "curve": "secp256k1",
         "i": 1,
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-        "shared_public_key": "03b61a18df2143a1e5514d1dc6ca9c607bd99cd4e769374e9dc8efece7f4eca56c",
+        "rid": "8cf312dae70d8169c4228ff933a1578c395403113277927e2bc2eb9e49bee07e",
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         "vss_setup": {
           "I": [
             {
@@ -11530,43 +10729,41 @@
           ],
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         "curve": "secp256k1",
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         "vss_setup": {
           "I": [
             {
@@ -11584,45 +10781,43 @@
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+      }
     }
   ],
   "t=Some(3),n=3,curve=secp256r1": [
     {
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+        "parties": [
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+          }
+        ],
+        "q": "bfb1a2c30ceb86af90922e070d04cdedbd4b2d0569c26906a4e78b81d615976bfd37e52cb545bc55dad1d24820af78cabaae98d49c1c95c9df072975f41f10c8eb0e5fecfb017a15dfa0d83d6a435e65eafec90bfad414931ff10752d0ac2236b04e5e8ae265c2bd5896b288302245478f7a9e275be8e247c6559b08a7d54ef3"
+      },
       "core": {
         "curve": "secp256r1",
         "i": 0,
         "public_shares": [
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-          "02c8c6476262816830c616fe871600f2cf616652ea09b892b0c727618118afcc11",
-          "024079f3f9557d5bed358d59ca89cd5fde5cbbb8cf26c4f61c6b8eb2e0b86b1a5c"
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+          "03415ac0bca60cc7d773ff7b76f832626721993f42624f8b657872de75dfac2ccd"
         ],
-        "rid": "26d3fc05671a21bc006ee7f7d9d38fbcc4cc669897ef05dea37117790111ec5e",
-        "shared_public_key": "0385b6c1705dc2bee2bebf4a1acf235f14ff3ed8a74391750a659b5305275c4eed",
+        "rid": "8c270c02fff035f4f27daf51b89a1e8320ca3c13974ca17b3fa7927ce5f33d48",
+        "shared_public_key": "03b85016b0747bed89d19df8c430ebb2133f3901da6ec214479ffd47172c769b61",
         "vss_setup": {
           "I": [
             {
@@ -11640,43 +10835,41 @@
           ],
           "min_signers": 3
         },
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           "I": [
             {
@@ -11694,43 +10887,41 @@
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-        "shared_public_key": "0385b6c1705dc2bee2bebf4a1acf235f14ff3ed8a74391750a659b5305275c4eed",
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+        "shared_public_key": "03b85016b0747bed89d19df8c430ebb2133f3901da6ec214479ffd47172c769b61",
         "vss_setup": {
           "I": [
             {
@@ -11748,47 +10939,55 @@
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       "core": {
         "curve": "secp256k1",
         "i": 0,
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         "vss_setup": {
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             {
@@ -11814,57 +11013,53 @@
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             {
@@ -11890,57 +11085,53 @@
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         "vss_setup": {
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             {
@@ -11966,57 +11157,53 @@
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         "curve": "secp256k1",
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         "vss_setup": {
           "I": [
             {
@@ -12042,57 +11229,53 @@
           ],
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         "curve": "secp256k1",
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         "vss_setup": {
           "I": [
             {
@@ -12118,59 +11301,55 @@
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   "t=Some(3),n=5,curve=secp256r1": [
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+      },
       "core": {
         "curve": "secp256r1",
         "i": 0,
         "public_shares": [
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-          "03272bb836ba9e327b8defdc559b9a7ce8c3bf492cc04a69158ab4e29a1b47417c",
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-        "rid": "73865ea924284457e42019b085426ff8d40b852d12da6625f02dcc87b9b37f8a",
-        "shared_public_key": "031c8783bae67f3373addfeed99927cc67d4edd210c45351136fbba85fc55556b0",
+          "029558d043604e4e6862ded7e230c6f021f1c7e98363ab4a359337eca514267c02",
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+          "0389c0c74ca0908a4b614c876bc2d2acbfb6700a208e62c73daca022d2ca6ae1d8"
+        ],
+        "rid": "07600efde047ade83d17ecc301a091449b4d0e8153b145f8dd33f160450a9a14",
+        "shared_public_key": "02aed85229f5c6864ddfc09f033d974f5633bca1baec8bd8ba5299c497bb0a0c20",
         "vss_setup": {
           "I": [
             {
@@ -12196,57 +11375,53 @@
           ],
           "min_signers": 3
         },
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             {
@@ -12272,57 +11447,53 @@
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         "curve": "secp256r1",
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         "vss_setup": {
           "I": [
             {
@@ -12348,57 +11519,53 @@
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             {
@@ -12424,57 +11591,53 @@
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         "vss_setup": {
           "I": [
             {
@@ -12500,61 +11663,67 @@
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             {
@@ -12588,71 +11757,65 @@
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         "vss_setup": {
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             {
@@ -12686,71 +11849,65 @@
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         "vss_setup": {
           "I": [
             {
@@ -12784,71 +11941,65 @@
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         "vss_setup": {
           "I": [
             {
@@ -12882,71 +12033,65 @@
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         "vss_setup": {
           "I": [
             {
@@ -12980,71 +12125,65 @@
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         "vss_setup": {
           "I": [
             {
@@ -13078,71 +12217,65 @@
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           "I": [
             {
@@ -13176,73 +12309,67 @@
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         "vss_setup": {
           "I": [
             {
@@ -13276,71 +12403,65 @@
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         "i": 1,
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         "vss_setup": {
           "I": [
             {
@@ -13374,71 +12495,65 @@
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         "vss_setup": {
           "I": [
             {
@@ -13472,71 +12587,65 @@
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         "vss_setup": {
           "I": [
             {
@@ -13570,71 +12679,65 @@
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         "vss_setup": {
           "I": [
             {
@@ -13668,71 +12771,65 @@
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         "curve": "secp256r1",
         "i": 5,
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         "vss_setup": {
           "I": [
             {
@@ -13766,71 +12863,65 @@
           ],
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         "vss_setup": {
           "I": [
             {
@@ -13864,76 +12955,85 @@
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           "min_signers": 3
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         "curve": "secp256k1",
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         "vss_setup": {
           "I": [
             {
@@ -13979,92 +13079,83 @@
           ],
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         },
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             {
@@ -14110,92 +13201,83 @@
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@@ -14241,92 +13323,83 @@
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@@ -14372,92 +13445,83 @@
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         "curve": "secp256k1",
         "i": 4,
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@@ -14503,92 +13567,83 @@
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         "curve": "secp256k1",
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         "vss_setup": {
           "I": [
             {
@@ -14634,92 +13689,83 @@
           ],
           "min_signers": 5
         },
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         "vss_setup": {
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             {
@@ -14765,92 +13811,83 @@
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@@ -14896,92 +13933,83 @@
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@@ -15025,94 +14053,85 @@
               "scalar": "000000000000000000000000000000000000000000000000000000000000000a"
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         "curve": "secp256k1",
         "i": 9,
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@@ -15158,94 +14177,85 @@
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       "core": {
         "curve": "secp256r1",
         "i": 0,
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         "vss_setup": {
           "I": [
             {
@@ -15291,92 +14301,83 @@
           ],
           "min_signers": 5
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         "vss_setup": {
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             {
@@ -15422,92 +14423,83 @@
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         "vss_setup": {
           "I": [
             {
@@ -15553,92 +14545,83 @@
           ],
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       "core": {
         "curve": "secp256r1",
         "i": 3,
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@@ -15684,92 +14667,83 @@
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       "core": {
         "curve": "secp256r1",
         "i": 4,
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         "vss_setup": {
           "I": [
             {
@@ -15815,92 +14789,83 @@
           ],
           "min_signers": 5
         },
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         "vss_setup": {
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             {
@@ -15946,92 +14911,83 @@
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             {
@@ -16077,92 +15033,83 @@
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       "core": {
         "curve": "secp256r1",
         "i": 7,
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@@ -16208,92 +15155,83 @@
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       "core": {
         "curve": "secp256r1",
         "i": 8,
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         "vss_setup": {
           "I": [
             {
@@ -16339,92 +15277,83 @@
           ],
           "min_signers": 5
         },
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         "vss_setup": {
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             {
@@ -16470,89 +15399,55 @@
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   ],
   "t=Some(5),n=5,curve=secp256k1": [
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           "I": [
             {
@@ -16578,57 +15473,53 @@
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       "core": {
         "curve": "secp256k1",
         "i": 1,
         "public_shares": [
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-        "shared_public_key": "0329bba4f5611e43a9f18468aa45131ed7a8f438c18859f0a01faaf04934463ba6",
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+          "03a383d8c8b60c35212bddafa26f81575e92ac207010b17524d0e7eb5afd783b2c"
+        ],
+        "rid": "9b00eaf83ecee912a6ae4ec335947faab90bbbd54d28ba09d1a146c323041731",
+        "shared_public_key": "031967862773c4c7b03c219cfed4d6dddce862f8dba9da0940d12c20258d0d50a3",
         "vss_setup": {
           "I": [
             {
@@ -16654,57 +15545,53 @@
           ],
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         "vss_setup": {
           "I": [
             {
@@ -16730,57 +15617,53 @@
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       "core": {
         "curve": "secp256k1",
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         "vss_setup": {
           "I": [
             {
@@ -16806,57 +15689,53 @@
           ],
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         },
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         "curve": "secp256k1",
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         "vss_setup": {
           "I": [
             {
@@ -16882,59 +15761,55 @@
           ],
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   "t=Some(5),n=5,curve=secp256r1": [
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       "core": {
         "curve": "secp256r1",
         "i": 0,
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         "vss_setup": {
           "I": [
             {
@@ -16960,57 +15835,53 @@
           ],
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           "I": [
             {
@@ -17036,57 +15907,53 @@
           ],
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             {
@@ -17112,57 +15979,53 @@
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           "I": [
             {
@@ -17188,57 +16051,53 @@
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           "I": [
             {
@@ -17264,61 +16123,67 @@
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         "curve": "secp256k1",
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@@ -17352,71 +16217,65 @@
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         "curve": "secp256k1",
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         "vss_setup": {
           "I": [
             {
@@ -17450,71 +16309,65 @@
           ],
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@@ -17545,74 +16398,68 @@
               "curve": "secp256k1",
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         "curve": "secp256k1",
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         "vss_setup": {
           "I": [
             {
@@ -17646,71 +16493,65 @@
           ],
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         "curve": "secp256k1",
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             {
@@ -17744,71 +16585,65 @@
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         "curve": "secp256k1",
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           "I": [
             {
@@ -17842,71 +16677,65 @@
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             {
@@ -17940,73 +16769,67 @@
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             {
@@ -18040,71 +16863,65 @@
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         "vss_setup": {
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             {
@@ -18138,71 +16955,65 @@
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         "vss_setup": {
           "I": [
             {
@@ -18236,71 +17047,65 @@
           ],
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         "vss_setup": {
           "I": [
             {
@@ -18334,71 +17139,65 @@
           ],
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         "vss_setup": {
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             {
@@ -18432,71 +17231,65 @@
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         "vss_setup": {
           "I": [
             {
@@ -18530,71 +17323,65 @@
           ],
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         "vss_setup": {
           "I": [
             {
@@ -18628,76 +17415,85 @@
           ],
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         "vss_setup": {
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             {
@@ -18743,92 +17539,83 @@
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         "vss_setup": {
           "I": [
             {
@@ -18874,92 +17661,83 @@
           ],
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       "core": {
         "curve": "secp256k1",
         "i": 2,
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@@ -19005,92 +17783,83 @@
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         "curve": "secp256k1",
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         "vss_setup": {
           "I": [
             {
@@ -19136,92 +17905,83 @@
           ],
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             {
@@ -19267,92 +18027,83 @@
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         "vss_setup": {
           "I": [
             {
@@ -19398,92 +18149,83 @@
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       "core": {
         "curve": "secp256k1",
         "i": 6,
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@@ -19529,92 +18271,83 @@
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       "core": {
         "curve": "secp256k1",
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         "vss_setup": {
           "I": [
             {
@@ -19660,92 +18393,83 @@
           ],
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@@ -19791,92 +18515,83 @@
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         "vss_setup": {
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             {
@@ -19922,94 +18637,85 @@
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   ],
   "t=Some(7),n=10,curve=secp256r1": [
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       "core": {
         "curve": "secp256r1",
         "i": 0,
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@@ -20055,92 +18761,83 @@
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+      },
       "core": {
         "curve": "secp256r1",
         "i": 1,
         "public_shares": [
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-        "shared_public_key": "03b63b5c09484c83e02d77b94c1aea93e5b3322331178468cbc14bb2bdc8252be0",
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+          "02281dbe5bbac609430706e5688e5deaf41859ea117fe9945c82ed942659e7c208"
+        ],
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+        "shared_public_key": "0363a8a1c0d79bf8a1675b33c84a2052397145180498b0744094408d3de94f454c",
         "vss_setup": {
           "I": [
             {
@@ -20186,92 +18883,83 @@
           ],
           "min_signers": 7
         },
-        "x": "b96e46574c73dfc281205cfb2d8f94c2ffd55693209152cb73dd321c884327ac"
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-      "parties": [
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         "curve": "secp256r1",
         "i": 2,
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         "vss_setup": {
           "I": [
             {
@@ -20317,92 +19005,83 @@
           ],
           "min_signers": 7
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         "vss_setup": {
           "I": [
             {
@@ -20448,92 +19127,83 @@
           ],
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         "vss_setup": {
           "I": [
             {
@@ -20579,92 +19249,83 @@
           ],
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       "core": {
         "curve": "secp256r1",
         "i": 5,
         "public_shares": [
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@@ -20710,92 +19371,83 @@
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+      },
       "core": {
         "curve": "secp256r1",
         "i": 6,
         "public_shares": [
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-        "shared_public_key": "03b63b5c09484c83e02d77b94c1aea93e5b3322331178468cbc14bb2bdc8252be0",
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+          "02281dbe5bbac609430706e5688e5deaf41859ea117fe9945c82ed942659e7c208"
+        ],
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+        "shared_public_key": "0363a8a1c0d79bf8a1675b33c84a2052397145180498b0744094408d3de94f454c",
         "vss_setup": {
           "I": [
             {
@@ -20841,92 +19493,83 @@
           ],
           "min_signers": 7
         },
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-      "parties": [
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+      },
       "core": {
         "curve": "secp256r1",
         "i": 7,
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+        ],
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         "vss_setup": {
           "I": [
             {
@@ -20972,92 +19615,83 @@
           ],
           "min_signers": 7
         },
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         "vss_setup": {
           "I": [
             {
@@ -21103,92 +19737,83 @@
           ],
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         "vss_setup": {
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@@ -21234,91 +19859,67 @@
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   "t=Some(7),n=7,curve=secp256k1": [
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             {
@@ -21352,71 +19953,65 @@
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             {
@@ -21450,71 +20045,65 @@
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         "vss_setup": {
           "I": [
             {
@@ -21548,71 +20137,65 @@
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         "curve": "secp256k1",
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         "vss_setup": {
           "I": [
             {
@@ -21646,71 +20229,65 @@
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             {
@@ -21744,71 +20321,65 @@
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         "curve": "secp256k1",
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             {
@@ -21842,71 +20413,65 @@
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             {
@@ -21940,73 +20505,67 @@
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             {
@@ -22040,71 +20599,65 @@
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         "curve": "secp256r1",
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         "vss_setup": {
           "I": [
             {
@@ -22138,71 +20691,65 @@
           ],
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         "curve": "secp256r1",
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         "vss_setup": {
           "I": [
             {
@@ -22236,71 +20783,65 @@
           ],
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         "curve": "secp256r1",
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         "vss_setup": {
           "I": [
             {
@@ -22334,71 +20875,65 @@
           ],
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         "curve": "secp256r1",
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         "vss_setup": {
           "I": [
             {
@@ -22432,71 +20967,65 @@
           ],
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         "curve": "secp256r1",
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         "vss_setup": {
           "I": [
             {
@@ -22530,71 +21059,65 @@
           ],
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             {
@@ -22628,55 +21151,8 @@
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-          "t": "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"
-        },
-        {
-          "N": "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",
-          "Y": "031386dd50f0449d4d0095105ac0d9cb00e9a3068ded8c7951f93f3cb753e71ae4",
-          "s": "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",
-          "t": "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"
-        },
-        {
-          "N": "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",
-          "Y": "0269be56e67cb8cc7fac61770cf39161890f8df0f0b413dd45b68d760ead4f51e9",
-          "s": "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",
-          "t": "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"
-        }
-      ],
-      "q": "83b3c316d17296365211a16f5ab64decd8f65d66a6e10a825c8b7c4b3eb8f0847fffb015b85ce2b8a7e4737c6abcfa8a7d2f3894e41bfa54956af01c70ed11e3a4bf78df392aed42d91632bc9409e19b542ccd9bc277410acbf41b47db7b58099f1dd265cda7379d8314b34a577b05af2fbb5da78b157b8be040d1d039574a63",
-      "y": "6495905335cbc986e904ff1fd7b9ae9fe15b1c4d27f46069a3726fa194bc6188"
+        "x": "a35f3f5c2bc87ac10e095c600107f2206aa95d10638def53cb37a19daa98b06e"
+      }
     }
   ]
 }
diff --git a/tests/src/bin/measure_perf.rs b/tests/src/bin/measure_perf.rs
index 2aa37c2..ffe89d1 100644
--- a/tests/src/bin/measure_perf.rs
+++ b/tests/src/bin/measure_perf.rs
@@ -52,8 +52,8 @@ async fn main() {
             let refresh_execution_id: [u8; 32] = rng.gen();
             let refresh_execution_id = ExecutionId::<E, L>::from_bytes(&refresh_execution_id);
 
-            use cggmp21::key_refresh::msg::Msg;
-            let mut simulation = Simulation::<Msg<E, D, L>>::new();
+            let mut simulation =
+                Simulation::<cggmp21::key_refresh::NonThresholdMsg<E, D, L>>::new();
 
             let mut primes = cggmp21_tests::CACHED_PRIMES.iter();
 
diff --git a/tests/tests/key_refresh.rs b/tests/tests/key_refresh.rs
index aec7535..20b0726 100644
--- a/tests/tests/key_refresh.rs
+++ b/tests/tests/key_refresh.rs
@@ -1,8 +1,8 @@
 #[generic_tests::define(attrs(tokio::test, test_case::case))]
 mod generic {
     use generic_ec::{hash_to_curve::FromHash, Point};
-    use rand::{Rng, SeedableRng};
-    use rand_chacha::ChaCha20Rng;
+    use rand::seq::SliceRandom;
+    use rand::Rng;
     use round_based::simulation::Simulation;
     use sha2::Sha256;
 
@@ -29,11 +29,11 @@ mod generic {
         let refresh_execution_id =
             ExecutionId::<E, ReasonablySecure>::from_bytes(&refresh_execution_id);
         let mut simulation =
-            Simulation::<cggmp21::key_refresh::msg::Msg<E, Sha256, ReasonablySecure>>::new();
+            Simulation::<cggmp21::key_refresh::NonThresholdMsg<E, Sha256, ReasonablySecure>>::new();
         let outputs = shares.iter().map(|share| {
             let party = simulation.add_party();
             let refresh_execution_id = refresh_execution_id.clone();
-            let mut party_rng = ChaCha20Rng::from_seed(rng.gen());
+            let mut party_rng = rng.fork();
             let pregenerated_data = primes.next().expect("Can't fetch primes");
             async move {
                 cggmp21::key_refresh(share, pregenerated_data)
@@ -86,7 +86,7 @@ mod generic {
         let outputs = key_shares.iter().map(|share| {
             let party = simulation.add_party();
             let signing_execution_id = signing_execution_id.clone();
-            let mut party_rng = ChaCha20Rng::from_seed(rng.gen());
+            let mut party_rng = rng.fork();
             async move {
                 cggmp21::signing(share.core.i, participants, share)
                     .set_execution_id(signing_execution_id)
@@ -105,6 +105,87 @@ mod generic {
         }
     }
 
+    #[test_case::case(2, 3; "t2n3")]
+    #[test_case::case(3, 5; "t3n5")]
+    #[tokio::test]
+    async fn aux_gen_works<E: generic_ec::Curve>(t: u16, n: u16)
+    where
+        generic_ec::Scalar<E>: FromHash,
+        Point<E>: generic_ec::coords::HasAffineX<E>,
+    {
+        let mut rng = rand_dev::DevRng::new();
+
+        let shares = cggmp21_tests::CACHED_SHARES
+            .get_shares::<E>(Some(t), n)
+            .expect("retrieve cached shares");
+        let mut primes = cggmp21_tests::CACHED_PRIMES.iter();
+
+        // Perform refresh
+
+        let refresh_execution_id: [u8; 32] = rng.gen();
+        let refresh_execution_id =
+            ExecutionId::<E, ReasonablySecure>::from_bytes(&refresh_execution_id);
+        let mut simulation = Simulation::<cggmp21::key_refresh::AuxOnlyMsg<Sha256>>::new();
+        let outputs = (0..n).map(|i| {
+            let party = simulation.add_party();
+            let refresh_execution_id = refresh_execution_id.clone();
+            let mut party_rng = rng.fork();
+            let pregenerated_data = primes.next().expect("Can't fetch primes");
+            async move {
+                cggmp21::aux_info_gen(i, n, pregenerated_data)
+                    .set_execution_id(refresh_execution_id)
+                    .start(&mut party_rng, party)
+                    .await
+            }
+        });
+
+        let aux_infos = futures::future::try_join_all(outputs)
+            .await
+            .expect("keygen failed");
+
+        // validate key shares
+
+        let key_shares = shares
+            .into_iter()
+            .zip(aux_infos.into_iter())
+            .map(|(share, aux)| share.update_aux(aux).unwrap())
+            .collect::<Vec<_>>();
+
+        // attempt to sign with new shares and verify the signature
+
+        let signing_execution_id = ExecutionId::<E, ReasonablySecure>::from_bytes(&[228; 32]);
+        let mut simulation = Simulation::<cggmp21::signing::msg::Msg<E, Sha256>>::new();
+        let message_to_sign = cggmp21::signing::DataToSign::digest::<Sha256>(&[42; 100]);
+
+        // choose t participants
+        let mut participants = (0..n).collect::<Vec<_>>();
+        participants.shuffle(&mut rng);
+        let participants = &participants[..usize::from(t)];
+        println!("Signers: {participants:?}");
+        let participants_shares = participants.iter().map(|i| &key_shares[usize::from(*i)]);
+
+        let outputs = participants_shares.zip(0..).map(|(share, i)| {
+            let party = simulation.add_party();
+            let signing_execution_id = signing_execution_id.clone();
+            let mut party_rng = rng.fork();
+            async move {
+                cggmp21::signing(i, participants, share)
+                    .set_execution_id(signing_execution_id)
+                    .sign(&mut party_rng, party, message_to_sign)
+                    .await
+            }
+        });
+        let signatures = futures::future::try_join_all(outputs)
+            .await
+            .expect("signing failed");
+
+        for signature in &signatures {
+            signature
+                .verify(&key_shares[0].core.shared_public_key, &message_to_sign)
+                .expect("signature is not valid");
+        }
+    }
+
     #[instantiate_tests(<cggmp21::supported_curves::Secp256r1>)]
     mod secp256r1 {}
     #[instantiate_tests(<cggmp21::supported_curves::Secp256k1>)]
diff --git a/tests/tests/pipeline.rs b/tests/tests/pipeline.rs
new file mode 100644
index 0000000..e9c5360
--- /dev/null
+++ b/tests/tests/pipeline.rs
@@ -0,0 +1,157 @@
+#[generic_tests::define(attrs(tokio::test, test_case::case))]
+mod generic {
+    use generic_ec::{hash_to_curve::FromHash, Curve, Point, Scalar};
+    use rand::{seq::SliceRandom, Rng};
+    use rand_dev::DevRng;
+    use round_based::simulation::Simulation;
+    use sha2::Sha256;
+
+    use cggmp21::keygen::ThresholdMsg;
+    use cggmp21::{
+        key_share::{AnyKeyShare, IncompleteKeyShare, KeyShare},
+        security_level::ReasonablySecure,
+        ExecutionId,
+    };
+
+    type Share<E> = KeyShare<E, ReasonablySecure>;
+    type Incomplete<E> = IncompleteKeyShare<E, ReasonablySecure>;
+
+    #[test_case::case(2, 3; "t2n3")]
+    #[test_case::case(4, 7; "t4n7")]
+    #[tokio::test]
+    async fn full_pipeline_works<E: Curve>(t: u16, n: u16)
+    where
+        Scalar<E>: FromHash,
+        Point<E>: generic_ec::coords::HasAffineX<E>,
+    {
+        let mut rng = DevRng::new();
+        let incomplete_shares = run_keygen(t, n, &mut rng).await;
+        let shares = run_refresh(incomplete_shares, &mut rng).await;
+        run_signing(&shares, &mut rng).await;
+    }
+
+    async fn run_keygen<E>(t: u16, n: u16, rng: &mut DevRng) -> Vec<Incomplete<E>>
+    where
+        E: Curve,
+        Scalar<E>: FromHash,
+    {
+        let keygen_execution_id: [u8; 32] = rng.gen();
+        let keygen_execution_id =
+            ExecutionId::<E, ReasonablySecure>::from_bytes(&keygen_execution_id);
+        let mut simulation = Simulation::<ThresholdMsg<E, ReasonablySecure, Sha256>>::new();
+
+        let mut outputs = vec![];
+        for i in 0..n {
+            let party = simulation.add_party();
+            let keygen_execution_id = keygen_execution_id.clone();
+            let mut party_rng = rng.fork();
+
+            outputs.push(async move {
+                cggmp21::keygen(i, n)
+                    .set_execution_id(keygen_execution_id)
+                    .set_threshold(t)
+                    .start(&mut party_rng, party)
+                    .await
+            })
+        }
+
+        futures::future::try_join_all(outputs)
+            .await
+            .expect("keygen failed")
+    }
+
+    async fn run_refresh<E>(shares: Vec<Incomplete<E>>, rng: &mut DevRng) -> Vec<Share<E>>
+    where
+        E: Curve,
+        Scalar<E>: FromHash,
+    {
+        let mut primes = cggmp21_tests::CACHED_PRIMES.iter();
+        let n = shares.len().try_into().unwrap();
+
+        let refresh_execution_id: [u8; 32] = rng.gen();
+        let refresh_execution_id =
+            ExecutionId::<E, ReasonablySecure>::from_bytes(&refresh_execution_id);
+        let mut simulation = Simulation::<cggmp21::key_refresh::AuxOnlyMsg<Sha256>>::new();
+
+        let outputs = (0..n).map(|i| {
+            let party = simulation.add_party();
+            let refresh_execution_id = refresh_execution_id.clone();
+            let mut party_rng = rng.fork();
+            let pregenerated_data = primes.next().expect("Can't fetch primes");
+            async move {
+                cggmp21::aux_info_gen(i, n, pregenerated_data)
+                    .set_execution_id(refresh_execution_id)
+                    .start(&mut party_rng, party)
+                    .await
+            }
+        });
+
+        let aux_infos = futures::future::try_join_all(outputs)
+            .await
+            .expect("keygen failed");
+
+        shares
+            .into_iter()
+            .zip(aux_infos.into_iter())
+            .map(|(core, aux)| Share::make(core, aux).expect("Couldn't make share from parts"))
+            .collect()
+    }
+
+    async fn run_signing<E>(shares: &[Share<E>], rng: &mut DevRng)
+    where
+        E: Curve,
+        Scalar<E>: FromHash,
+        Point<E>: generic_ec::coords::HasAffineX<E>,
+    {
+        use rand::RngCore;
+
+        let t = shares[0].min_signers();
+        let n = shares.len().try_into().unwrap();
+
+        let signing_execution_id: [u8; 32] = rng.gen();
+        let signing_execution_id =
+            ExecutionId::<E, ReasonablySecure>::from_bytes(&signing_execution_id);
+        let mut simulation = Simulation::<cggmp21::signing::msg::Msg<E, Sha256>>::new();
+
+        let mut original_message_to_sign = [0u8; 100];
+        rng.fill_bytes(&mut original_message_to_sign);
+        let message_to_sign =
+            cggmp21::signing::DataToSign::digest::<Sha256>(&original_message_to_sign);
+
+        // Choose `t` signers to perform signing
+        let mut participants = (0..n).collect::<Vec<_>>();
+        participants.shuffle(rng);
+        let participants = &participants[..usize::from(t)];
+        println!("Signers: {participants:?}");
+        let participants_shares = participants.iter().map(|i| &shares[usize::from(*i)]);
+
+        let mut outputs = vec![];
+        for (i, share) in (0..).zip(participants_shares) {
+            let party = simulation.add_party();
+            let signing_execution_id = signing_execution_id.clone();
+            let mut party_rng = rng.fork();
+
+            outputs.push(async move {
+                cggmp21::signing(i, participants, share)
+                    .set_execution_id(signing_execution_id)
+                    .sign(&mut party_rng, party, message_to_sign)
+                    .await
+            });
+        }
+
+        let signatures = futures::future::try_join_all(outputs)
+            .await
+            .expect("signing failed");
+
+        signatures[0]
+            .verify(&shares[0].core.shared_public_key, &message_to_sign)
+            .expect("signature is not valid");
+
+        assert!(signatures.iter().all(|s_i| signatures[0] == *s_i));
+    }
+
+    #[instantiate_tests(<cggmp21::supported_curves::Secp256r1>)]
+    mod secp256r1 {}
+    #[instantiate_tests(<cggmp21::supported_curves::Secp256k1>)]
+    mod secp256k1 {}
+}